ग्राफ (y=3-|x-2|) का अधिकतम मान क्या है?
What is the maximum value of the graph (y=3-|x-2|)?
#graphs
#modulus
#maximum
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (3)
B (2)
C (0)
D (5)
Explanation opens after your attempt
Step 1
Concept
The minimum value of (|x-2|) is (0), so the maximum value of (y) is (3). An inverted modulus graph gives its maximum at the vertex.
Step 2
Why this answer is correct
The correct answer is A. (3). The minimum value of (|x-2|) is (0), so the maximum value of (y) is (3). An inverted modulus graph gives its maximum at the vertex.
Step 3
Exam Tip
(|x-2|) का न्यूनतम मान (0) है इसलिए (y) का अधिकतम मान (3) है। उल्टा मापांक ग्राफ शीर्ष पर अधिकतम देता है।
Login to save your score, XP, coins and progress. Login
फलन \(y=\sqrt{|x|}\) के ग्राफ के लिए कौन सा कथन सही है?
Which statement is correct for the graph of \(y=\sqrt{|x|}\)?
#graphs
#square-root
#modulus
#symmetry
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A यह (y)-अक्ष के सापेक्ष सममित है / It is symmetric about the (y)-axis
B यह केवल \(x\ge 0\) के लिए परिभाषित है / It is defined only for \(x\ge 0\)
C इसकी रेंज (\(-\infty,0]\) है / Its range is (\(-\infty,0]\)
D यह मूल बिंदु के सापेक्ष सममित है / It is symmetric about the origin
Explanation opens after your attempt
Correct Answer
A. यह (y)-अक्ष के सापेक्ष सममित है / It is symmetric about the (y)-axis
Step 1
Concept
Since (|-x|=|x|), we get (f(-x)=f(x)). Therefore the graph is symmetric about the (y)-axis.
Step 2
Why this answer is correct
The correct answer is A. यह (y)-अक्ष के सापेक्ष सममित है / It is symmetric about the (y)-axis. Since (|-x|=|x|), we get (f(-x)=f(x)). Therefore the graph is symmetric about the (y)-axis.
Step 3
Exam Tip
क्योंकि (|-x|=|x|) है इसलिए (f(-x)=f(x)) मिलता है। इसलिए ग्राफ (y)-अक्ष के सापेक्ष सममित होता है।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=|x+4|-2) के ग्राफ का शीर्ष बिंदु कौन सा है?
Which point is the vertex of the graph of (f(x)=|x+4|-2)?
#graphs
#modulus
#vertex
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ((-4,-2))
B ((4,-2))
C ((-2,-4))
D ((0,-2))
Explanation opens after your attempt
Correct Answer
A. ((-4,-2))
Step 1
Concept
Set the inside of the modulus (x+4=0), so (x=-4). Then (y=-2), so the vertex is ((-4,-2)).
Step 2
Why this answer is correct
The correct answer is A. ((-4,-2)). Set the inside of the modulus (x+4=0), so (x=-4). Then (y=-2), so the vertex is ((-4,-2)).
Step 3
Exam Tip
मापांक के अंदर (x+4=0) करने पर (x=-4) मिलता है। तब (y=-2) है इसलिए शीर्ष ((-4,-2)) है।
Login to save your score, XP, coins and progress. Login
ग्राफ \(y=\frac{x^2-4}{x-2}\) में (x=2) पर क्या होता है?
What happens at (x=2) in the graph of \(y=\frac{x^2-4}{x-2}\)?
#graphs
#rational
#hole
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A छिद्र बनता है / A hole occurs
B ऊर्ध्वाधर आसम्टोट बनता है / A vertical asymptote occurs
C ग्राफ (y=0) बनता है / The graph becomes (y=0)
D ग्राफ पर बिंदु ((2,0)) होता है / The point ((2,0)) lies on the graph
Explanation opens after your attempt
Correct Answer
A. छिद्र बनता है / A hole occurs
Step 1
Concept
(\frac{x-2 -4}{x-2}=\frac{(x-2)(x+2)}{x-2}), but (x=2) remains excluded. So the graph is like (y=x+2) with a hole at (x=2).
Step 2
Why this answer is correct
The correct answer is A. छिद्र बनता है / A hole occurs. (\frac{x-2 -4}{x-2}=\frac{(x-2)(x+2)}{x-2}), but (x=2) remains excluded. So the graph is like (y=x+2) with a hole at (x=2).
Step 3
Exam Tip
(\frac{x-2 -4}{x-2}=\frac{(x-2)(x+2)}{x-2}) है पर (x=2) निषिद्ध रहता है। इसलिए ग्राफ (y=x+2) जैसा है लेकिन (x=2) पर छिद्र है।
Login to save your score, XP, coins and progress. Login
फलन (y=|x-5|+2) की रेंज क्या है?
What is the range of the function (y=|x-5|+2)?
#graphs
#modulus
#range
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \([2,\infty\))
B \([5,\infty\))
C (\(-\infty,2]\)
D \(\mathbb{R}\)
Explanation opens after your attempt
Correct Answer
A. \([2,\infty\))
Step 1
Concept
Since \(|x-5|\ge 0\), we get \(y\ge 2\). For range, first check the minimum value.
Step 2
Why this answer is correct
The correct answer is A. \([2,\infty\)). Since \(|x-5|\ge 0\), we get \(y\ge 2\). For range, first check the minimum value.
Step 3
Exam Tip
\(|x-5|\ge 0\) होता है इसलिए \(y\ge 2\) है। रेंज निकालते समय न्यूनतम मान पहले देखें।
Login to save your score, XP, coins and progress. Login
फलन (y=|x-1|-|x+3|) का (x>1) के लिए मान क्या होगा?
For (x>1), what is the value of (y=|x-1|-|x+3|)?
#graphs
#modulus
#piecewise
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (y=-4)
B (y=4)
C (y=2x+2)
D (y=-2x-2)
Explanation opens after your attempt
Step 1
Concept
For (x>1), (|x-1|=x-1) and (|x+3|=x+3). Therefore (y=(x-1)-(x+3)=-4).
Step 2
Why this answer is correct
The correct answer is A. (y=-4). For (x>1), (|x-1|=x-1) and (|x+3|=x+3). Therefore (y=(x-1)-(x+3)=-4).
Step 3
Exam Tip
(x>1) पर (|x-1|=x-1) और (|x+3|=x+3) है। इसलिए (y=(x-1)-(x+3)=-4) मिलता है।
Login to save your score, XP, coins and progress. Login
फलन (y=2|x+1|-6) का (x)-अक्ष से प्रतिच्छेद किन बिंदुओं पर है?
At which points does the graph (y=2|x+1|-6) intersect the (x)-axis?
#graphs
#modulus
#intercepts
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ((-4,0)) और ((2,0)) / ((-4,0)) and ((2,0))
B ((-1,0)) और ((6,0)) / ((-1,0)) and ((6,0))
C ((0,-4)) और ((0,2)) / ((0,-4)) and ((0,2))
D ((4,0)) और ((-2,0)) / ((4,0)) and ((-2,0))
Explanation opens after your attempt
Correct Answer
A. ((-4,0)) और ((2,0)) / ((-4,0)) and ((2,0))
Step 1
Concept
From (2|x+1|-6=0), we get (|x+1|=3). Hence (x=-4) or (x=2).
Step 2
Why this answer is correct
The correct answer is A. ((-4,0)) और ((2,0)) / ((-4,0)) and ((2,0)). From (2|x+1|-6=0), we get (|x+1|=3). Hence (x=-4) or (x=2).
Step 3
Exam Tip
(2|x+1|-6=0) से (|x+1|=3) मिलता है। इसलिए (x=-4) या (x=2) है।
Login to save your score, XP, coins and progress. Login
ग्राफ (y=|x+5|+|x-1|) किस अंतराल पर स्थिर रहता है?
On which interval is the graph (y=|x+5|+|x-1|) constant?
#graphs
#modulus
#piecewise
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(-5\le x\le 1\)
B \(x\le -5\)
C \(x\ge 1\)
D \(1\le x\le 5\)
Explanation opens after your attempt
Correct Answer
A. \(-5\le x\le 1\)
Step 1
Concept
On \(-5\le x\le 1\), the sum is ((x+5)+(1-x)=6). In such graphs, the part between the two zero points is horizontal.
Step 2
Why this answer is correct
The correct answer is A. \(-5\le x\le 1\). On \(-5\le x\le 1\), the sum is ((x+5)+(1-x)=6). In such graphs, the part between the two zero points is horizontal.
Step 3
Exam Tip
\(-5\le x\le 1\) पर योग ((x+5)+(1-x)=6) होता है। ऐसे ग्राफ में दोनों शून्य बिंदुओं के बीच भाग क्षैतिज होता है।
Login to save your score, XP, coins and progress. Login
फलन \(y=|x^2-9|\) का न्यूनतम मान क्या है?
What is the minimum value of \(y=|x^2-9|\)?
#graphs
#modulus
#quadratic
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (0)
B (3)
C (9)
D (1)
Explanation opens after your attempt
Step 1
Concept
The minimum value of a modulus can be (0) when \(x^2-9=0\). Here \(x=\pm3\) gives value (0).
Step 2
Why this answer is correct
The correct answer is A. (0). The minimum value of a modulus can be (0) when \(x^2-9=0\). Here \(x=\pm3\) gives value (0).
Step 3
Exam Tip
मापांक का न्यूनतम मान (0) हो सकता है जब \(x^2-9=0\)। यहां \(x=\pm3\) पर मान (0) मिलता है।
Login to save your score, XP, coins and progress. Login
फलन \(y=x^2+4x+1\) के ग्राफ का शीर्ष बिंदु कौन सा है?
What is the vertex of the graph \(y=x^2+4x+1\)?
#graphs
#quadratic
#vertex
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ((-2,-3))
B ((2,-3))
C ((-4,1))
D ((0,1))
Explanation opens after your attempt
Correct Answer
A. ((-2,-3))
Step 1
Concept
Completing the square gives (y=(x+2)2 -3). Therefore the vertex is ((-2,-3)).
Step 2
Why this answer is correct
The correct answer is A. ((-2,-3)). Completing the square gives (y=(x+2)2 -3). Therefore the vertex is ((-2,-3)).
Step 3
Exam Tip
पूर्ण वर्ग बनाने पर (y=(x+2)2 -3) मिलता है। इसलिए शीर्ष ((-2,-3)) है।
Login to save your score, XP, coins and progress. Login
परवलय (y=-2(x+3)2 +7) की सममिति अक्ष कौन सी है?
What is the axis of symmetry of the parabola (y=-2(x+3)2 +7)?
#graphs
#quadratic
#axis
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (x=-3)
B (x=3)
C (y=7)
D (y=-2)
Explanation opens after your attempt
Step 1
Concept
In (y=a(x-h)2 +k), the axis is (x=h). Here (h=-3).
Step 2
Why this answer is correct
The correct answer is A. (x=-3). In (y=a(x-h)2 +k), the axis is (x=h). Here (h=-3).
Step 3
Exam Tip
(y=a(x-h)2 +k) में अक्ष (x=h) होती है। यहां (h=-3) है।
Login to save your score, XP, coins and progress. Login
फलन (y=4-(x-1)2 ) की रेंज क्या है?
What is the range of (y=4-(x-1)2 )?
#graphs
#quadratic
#range
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (\(-\infty,4]\)
B \([4,\infty\))
C (\(-\infty,1]\)
D \(\mathbb{R}\)
Explanation opens after your attempt
Correct Answer
A. (\(-\infty,4]\)
Step 1
Concept
Since (-(x-1)2 \le 0), we get \(y\le 4\). A downward parabola gives its maximum at the vertex.
Step 2
Why this answer is correct
The correct answer is A. (\(-\infty,4]\). Since (-(x-1)2 \le 0), we get \(y\le 4\). A downward parabola gives its maximum at the vertex.
Step 3
Exam Tip
(-(x-1)2 \le 0) होता है इसलिए \(y\le 4\) है। नीचे खुलने वाले परवलय में शीर्ष अधिकतम देता है।
Login to save your score, XP, coins and progress. Login
ग्राफ \(y=x^2-8x+15\) (x)-अक्ष को किन (x) मानों पर काटता है?
At which (x) values does the graph \(y=x^2-8x+15\) cut the (x)-axis?
#graphs
#quadratic
#zeros
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (x=3,5)
B (x=-3,-5)
C (x=1,15)
D (x=0,8)
Explanation opens after your attempt
Correct Answer
A. (x=3,5)
Step 1
Concept
Set (y=0) on the (x)-axis. From \(x^2-8x+15=0\), we get (x=3,5).
Step 2
Why this answer is correct
The correct answer is A. (x=3,5). Set (y=0) on the (x)-axis. From \(x^2-8x+15=0\), we get (x=3,5).
Step 3
Exam Tip
(x)-अक्ष पर (y=0) रखें। \(x^2-8x+15=0\) से (x=3,5) मिलता है।
Login to save your score, XP, coins and progress. Login
फलन (y=(x+1)2 -9) का (y)-अक्ष से प्रतिच्छेद क्या है?
What is the (y)-intercept of (y=(x+1)2 -9)?
#graphs
#quadratic
#intercept
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ((0,-8))
B ((-1,-9))
C ((0,9))
D ((8,0))
Explanation opens after your attempt
Correct Answer
A. ((0,-8))
Step 1
Concept
On the (y)-axis, (x=0). Then (y=(1)2 -9=-8).
Step 2
Why this answer is correct
The correct answer is A. ((0,-8)). On the (y)-axis, (x=0). Then (y=(1)2 -9=-8).
Step 3
Exam Tip
(y)-अक्ष पर (x=0) होता है। तब (y=(1)2 -9=-8) मिलता है।
Login to save your score, XP, coins and progress. Login
रेखा (y=-4x+9) का ढाल क्या है?
What is the slope of the line (y=-4x+9)?
#graphs
#linear
#slope
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (-4)
B (4)
C (9)
D (-9)
Explanation opens after your attempt
Step 1
Concept
In the line (y=mx+c), (m) is the slope. Here (m=-4).
Step 2
Why this answer is correct
The correct answer is A. (-4). In the line (y=mx+c), (m) is the slope. Here (m=-4).
Step 3
Exam Tip
रेखा (y=mx+c) में (m) ढाल होता है। यहां (m=-4) है।
Login to save your score, XP, coins and progress. Login
रेखा (2x-5y=10) का (y)-अक्ष से प्रतिच्छेद क्या है?
What is the (y)-intercept of the line (2x-5y=10)?
#graphs
#linear
#intercept
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ((0,-2))
B ((0,2))
C ((5,0))
D ((-5,0))
Explanation opens after your attempt
Correct Answer
A. ((0,-2))
Step 1
Concept
For the (y)-axis, set (x=0). From (-5y=10), we get (y=-2).
Step 2
Why this answer is correct
The correct answer is A. ((0,-2)). For the (y)-axis, set (x=0). From (-5y=10), we get (y=-2).
Step 3
Exam Tip
(y)-अक्ष के लिए (x=0) रखें। (-5y=10) से (y=-2) मिलता है।
Login to save your score, XP, coins and progress. Login
रेखा (x=-7) के ग्राफ के लिए सही कथन कौन सा है?
Which statement is correct for the graph of the line (x=-7)?
#graphs
#linear
#vertical-line
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A यह (y)-अक्ष के समानांतर रेखा है / It is parallel to the (y)-axis
B यह (x)-अक्ष के समानांतर रेखा है / It is parallel to the (x)-axis
C यह मूल बिंदु से गुजरती है / It passes through the origin
D यह (y=x) है / It is (y=x)
Explanation opens after your attempt
Correct Answer
A. यह (y)-अक्ष के समानांतर रेखा है / It is parallel to the (y)-axis
Step 1
Concept
In (x=-7), (x) is fixed and (y) can be any value. Hence it is a vertical line.
Step 2
Why this answer is correct
The correct answer is A. यह (y)-अक्ष के समानांतर रेखा है / It is parallel to the (y)-axis. In (x=-7), (x) is fixed and (y) can be any value. Hence it is a vertical line.
Step 3
Exam Tip
(x=-7) में (x) स्थिर है और (y) कोई भी हो सकता है। इसलिए यह ऊर्ध्वाधर रेखा है।
Login to save your score, XP, coins and progress. Login
फलन (y=0) के ग्राफ के बारे में कौन सा कथन सही है?
Which statement is correct about the graph of (y=0)?
#graphs
#constant
#axis
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A यह (x)-अक्ष है / It is the (x)-axis
B यह (y)-अक्ष है / It is the (y)-axis
C यह रेखा (x=0) है / It is the line (x=0)
D यह परवलय है / It is a parabola
Explanation opens after your attempt
Correct Answer
A. यह (x)-अक्ष है / It is the (x)-axis
Step 1
Concept
For (y=0), all points lie on the (x)-axis. The zero constant function has the (x)-axis as its graph.
Step 2
Why this answer is correct
The correct answer is A. यह (x)-अक्ष है / It is the (x)-axis. For (y=0), all points lie on the (x)-axis. The zero constant function has the (x)-axis as its graph.
Step 3
Exam Tip
(y=0) पर सभी बिंदु (x)-अक्ष पर होते हैं। स्थिर शून्य फलन का ग्राफ (x)-अक्ष है।
Login to save your score, XP, coins and progress. Login
फलन \(y=\sqrt{x-6}\) का डोमेन क्या है?
What is the domain of \(y=\sqrt{x-6}\)?
#graphs
#square-root
#domain
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \([6,\infty\))
B (\(6,\infty\))
C (\(-\infty,6]\)
D \(\mathbb{R}\)
Explanation opens after your attempt
Correct Answer
A. \([6,\infty\))
Step 1
Concept
For the square root, \(x-6\ge 0\) must hold. Hence \(x\ge 6\).
Step 2
Why this answer is correct
The correct answer is A. \([6,\infty\)). For the square root, \(x-6\ge 0\) must hold. Hence \(x\ge 6\).
Step 3
Exam Tip
वर्गमूल के लिए \(x-6\ge 0\) होना चाहिए। इसलिए \(x\ge 6\) है।
Login to save your score, XP, coins and progress. Login
फलन \(y=5-\sqrt{x+2}\) का प्रारंभिक बिंदु कौन सा है?
What is the starting point of the graph \(y=5-\sqrt{x+2}\)?
#graphs
#square-root
#start-point
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ((-2,5))
B ((2,5))
C ((5,-2))
D ((0,5))
Explanation opens after your attempt
Correct Answer
A. ((-2,5))
Step 1
Concept
The expression inside the square root starts at (x+2=0). Then (y=5), so the point is ((-2,5)).
Step 2
Why this answer is correct
The correct answer is A. ((-2,5)). The expression inside the square root starts at (x+2=0). Then (y=5), so the point is ((-2,5)).
Step 3
Exam Tip
वर्गमूल का अंदरूनी भाग (x+2=0) पर शुरू होता है। तब (y=5) है इसलिए बिंदु ((-2,5)) है।
Login to save your score, XP, coins and progress. Login
फलन \(y=\sqrt{16-x^2}\) का डोमेन क्या है?
What is the domain of \(y=\sqrt{16-x^2}\)?
#graphs
#square-root
#domain
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ([-4,4])
B (\(-\infty,-4]\cup[4,\infty\))
C ([0,4])
D \(\mathbb{R}\)
Explanation opens after your attempt
Correct Answer
A. ([-4,4])
Step 1
Concept
For the square root, \(16-x^2\ge 0\) is required. This gives \(-4\le x\le 4\).
Step 2
Why this answer is correct
The correct answer is A. ([-4,4]). For the square root, \(16-x^2\ge 0\) is required. This gives \(-4\le x\le 4\).
Step 3
Exam Tip
वर्गमूल के लिए \(16-x^2\ge 0\) चाहिए। इससे \(-4\le x\le 4\) मिलता है।
Login to save your score, XP, coins and progress. Login
ग्राफ \(y=\sqrt{16-x^2}\) की रेंज क्या है?
What is the range of the graph \(y=\sqrt{16-x^2}\)?
#graphs
#circle
#range
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ([0,4])
B ([-4,4])
C (\(-\infty,4]\)
D \([4,\infty\))
Explanation opens after your attempt
Correct Answer
A. ([0,4])
Step 1
Concept
It is the upper semicircle of \(x^2+y^2=16\). Hence (y) ranges from (0) to (4).
Step 2
Why this answer is correct
The correct answer is A. ([0,4]). It is the upper semicircle of \(x^2+y^2=16\). Hence (y) ranges from (0) to (4).
Step 3
Exam Tip
यह वृत्त \(x^2+y^2=16\) का ऊपरी अर्धभाग है। इसलिए (y) का मान (0) से (4) तक है।
Login to save your score, XP, coins and progress. Login
फलन \(y=\frac{1}{x+5}\) के ग्राफ का ऊर्ध्वाधर आसम्टोट क्या है?
What is the vertical asymptote of the graph \(y=\frac{1}{x+5}\)?
#graphs
#rational
#asymptote
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (x=-5)
B (x=5)
C (y=0)
D (y=-5)
Explanation opens after your attempt
Step 1
Concept
The denominator (x+5) makes the function undefined when it is zero. Therefore (x=-5) is the vertical asymptote.
Step 2
Why this answer is correct
The correct answer is A. (x=-5). The denominator (x+5) makes the function undefined when it is zero. Therefore (x=-5) is the vertical asymptote.
Step 3
Exam Tip
हर (x+5) शून्य होने पर फलन अपरिभाषित हो जाता है। इसलिए (x=-5) ऊर्ध्वाधर आसम्टोट है।
Login to save your score, XP, coins and progress. Login
फलन \(y=\frac{3}{x-2}+4\) के ग्राफ का क्षैतिज आसम्टोट क्या है?
What is the horizontal asymptote of \(y=\frac{3}{x-2}+4\)?
#graphs
#rational
#horizontal-asymptote
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (y=4)
B (x=2)
C (y=3)
D (x=4)
Explanation opens after your attempt
Step 1
Concept
The term \(\frac{3}{x-2}\) approaches (0) for large (|x|). Hence the graph approaches (y=4).
Step 2
Why this answer is correct
The correct answer is A. (y=4). The term \(\frac{3}{x-2}\) approaches (0) for large (|x|). Hence the graph approaches (y=4).
Step 3
Exam Tip
\(\frac{3}{x-2}\) बड़े (|x|) पर (0) के पास जाता है। इसलिए ग्राफ (y=4) के पास जाता है।
Login to save your score, XP, coins and progress. Login
फलन \(y=\frac{x-1}{x+2}\) के ग्राफ में कौन सा (x) मान डोमेन में नहीं है?
Which (x) value is not in the domain of \(y=\frac{x-1}{x+2}\)?
#graphs
#rational
#domain
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (x=-2)
B (x=1)
C (x=0)
D (x=2)
Explanation opens after your attempt
Step 1
Concept
The denominator (x+2) cannot be zero. From (x+2=0), (x=-2) is excluded.
Step 2
Why this answer is correct
The correct answer is A. (x=-2). The denominator (x+2) cannot be zero. From (x+2=0), (x=-2) is excluded.
Step 3
Exam Tip
हर (x+2) शून्य नहीं हो सकता। (x+2=0) से (x=-2) निषिद्ध है।
Login to save your score, XP, coins and progress. Login
फलन \(y=\frac{2x+1}{x-3}\) का क्षैतिज आसम्टोट क्या है?
What is the horizontal asymptote of \(y=\frac{2x+1}{x-3}\)?
#graphs
#rational
#horizontal-asymptote
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (y=2)
B (x=3)
C (y=1)
D (y=-3)
Explanation opens after your attempt
Step 1
Concept
The numerator and denominator have equal degree, so take the ratio of leading coefficients. Since \(\frac{2}{1}=2\), the asymptote is (y=2).
Step 2
Why this answer is correct
The correct answer is A. (y=2). The numerator and denominator have equal degree, so take the ratio of leading coefficients. Since \(\frac{2}{1}=2\), the asymptote is (y=2).
Step 3
Exam Tip
अंश और हर की डिग्री समान है इसलिए प्रमुख गुणांकों का अनुपात लें। \(\frac{2}{1}=2\) से आसम्टोट (y=2) है।
Login to save your score, XP, coins and progress. Login
फलन \(y=\frac{1}{x^2+4}\) के ग्राफ की रेंज क्या है?
What is the range of \(y=\frac{1}{x^2+4}\)?
#graphs
#rational
#range
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (\(0,\frac{1}{4}]\)
B \([0,\frac{1}{4}]\)
C \([4,\infty\))
D \(\mathbb{R}\)
Explanation opens after your attempt
Correct Answer
A. (\(0,\frac{1}{4}]\)
Step 1
Concept
Since \(x^2+4\ge 4\), the maximum value is \(\frac{1}{4}\). The graph approaches (0) but never takes (0).
Step 2
Why this answer is correct
The correct answer is A. (\(0,\frac{1}{4}]\). Since \(x^2+4\ge 4\), the maximum value is \(\frac{1}{4}\). The graph approaches (0) but never takes (0).
Step 3
Exam Tip
\(x^2+4\ge 4\) इसलिए अधिकतम मान \(\frac{1}{4}\) है। ग्राफ (0) के पास जाता है पर (0) नहीं लेता।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=\frac{x-2 -1}{x-2 +1}) के ग्राफ की सममिति कौन सी है?
What is the symmetry of the graph of (f(x)=\frac{x-2 -1}{x-2 +1})?
#graphs
#rational
#symmetry
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (y)-अक्ष के सापेक्ष सममिति / Symmetry about the (y)-axis
B मूल बिंदु के सापेक्ष सममिति / Symmetry about the origin
C (x)-अक्ष के सापेक्ष सममिति / Symmetry about the (x)-axis
D कोई सममिति नहीं / No symmetry
Explanation opens after your attempt
Correct Answer
A. (y)-अक्ष के सापेक्ष सममिति / Symmetry about the (y)-axis
Step 1
Concept
(f(-x)=\frac{x-2 -1}{x-2 +1}=f(x)). Therefore it is an even function.
Step 2
Why this answer is correct
The correct answer is A. (y)-अक्ष के सापेक्ष सममिति / Symmetry about the (y)-axis. (f(-x)=\frac{x-2 -1}{x-2 +1}=f(x)). Therefore it is an even function.
Step 3
Exam Tip
(f(-x)=\frac{x-2 -1}{x-2 +1}=f(x)) है। इसलिए यह सम फलन है।
Login to save your score, XP, coins and progress. Login
ग्राफ \(y=x^3+2\) (y)-अक्ष को किस बिंदु पर काटता है?
At which point does the graph \(y=x^3+2\) cut the (y)-axis?
#graphs
#cubic
#intercept
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ((0,2))
B ((2,0))
C ((0,-2))
D ((1,3))
Explanation opens after your attempt
Correct Answer
A. ((0,2))
Step 1
Concept
On the (y)-axis, set (x=0). Then \(y=0^3+2=2\).
Step 2
Why this answer is correct
The correct answer is A. ((0,2)). On the (y)-axis, set (x=0). Then \(y=0^3+2=2\).
Step 3
Exam Tip
(y)-अक्ष पर (x=0) रखें। तब \(y=0^3+2=2\) मिलता है।
Login to save your score, XP, coins and progress. Login
फलन (y=(x+2)3 -1) में \(y=x^3\) का बिंदु ((0,0)) किस बिंदु पर जाता है?
In (y=(x+2)3 -1), where does the point ((0,0)) of \(y=x^3\) move?
#graphs
#transformation
#cubic
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ((-2,-1))
B ((2,-1))
C ((-2,1))
D ((1,-2))
Explanation opens after your attempt
Correct Answer
A. ((-2,-1))
Step 1
Concept
The term (x+2) shifts the graph (2) units left and (-1) shifts it down. Hence ((0,0)) becomes ((-2,-1)).
Step 2
Why this answer is correct
The correct answer is A. ((-2,-1)). The term (x+2) shifts the graph (2) units left and (-1) shifts it down. Hence ((0,0)) becomes ((-2,-1)).
Step 3
Exam Tip
(x+2) ग्राफ को (2) इकाई बाईं ओर और (-1) नीचे ले जाता है। इसलिए ((0,0)) से ((-2,-1)) मिलता है।
Login to save your score, XP, coins and progress. Login
फलन \(y=-x^3\) का ग्राफ \(y=x^3\) से कैसे प्राप्त होगा?
How is the graph \(y=-x^3\) obtained from \(y=x^3\)?
#graphs
#cubic
#reflection
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (x)-अक्ष में परावर्तन / Reflection in the (x)-axis
B (y)-अक्ष में परावर्तन / Reflection in the (y)-axis
C (1) इकाई ऊपर खिसकाव / Shift (1) unit up
D (1) इकाई दाईं ओर खिसकाव / Shift (1) unit right
Explanation opens after your attempt
Correct Answer
A. (x)-अक्ष में परावर्तन / Reflection in the (x)-axis
Step 1
Concept
The outside negative sign reverses all (y)-values. Therefore the graph is reflected in the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. (x)-अक्ष में परावर्तन / Reflection in the (x)-axis. The outside negative sign reverses all (y)-values. Therefore the graph is reflected in the (x)-axis.
Step 3
Exam Tip
बाहर का ऋण चिह्न सभी (y)-मानों को विपरीत कर देता है। इसलिए (x)-अक्ष में परावर्तन होता है।
Login to save your score, XP, coins and progress. Login
फलन (y=(-x)3 ) का ग्राफ \(y=x^3\) से कैसे संबंधित है?
How is (y=(-x)3 ) related to \(y=x^3\)?
#graphs
#cubic
#reflection
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (y)-अक्ष में परावर्तन / Reflection in the (y)-axis
B (x)-अक्ष में परावर्तन / Reflection in the (x)-axis
C ऊपर खिसकाव / Upward shift
D दाईं ओर खिसकाव / Right shift
Explanation opens after your attempt
Correct Answer
A. (y)-अक्ष में परावर्तन / Reflection in the (y)-axis
Step 1
Concept
Replacing (x) by (-x) reflects the graph in the (y)-axis. Here (y=(-x)3 =-x-3 ) also holds.
Step 2
Why this answer is correct
The correct answer is A. (y)-अक्ष में परावर्तन / Reflection in the (y)-axis. Replacing (x) by (-x) reflects the graph in the (y)-axis. Here (y=(-x)3 =-x-3 ) also holds.
Step 3
Exam Tip
(x) की जगह (-x) आने से (y)-अक्ष में परावर्तन होता है। यहां (y=(-x)3 =-x-3 ) भी है।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=x-5 ) के ग्राफ की सममिति कौन सी है?
What is the symmetry of the graph of (f(x)=x-5 )?
#graphs
#power-function
#symmetry
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A मूल बिंदु के सापेक्ष सममिति / Symmetry about the origin
B (y)-अक्ष के सापेक्ष सममिति / Symmetry about the (y)-axis
C (x)-अक्ष के सापेक्ष सममिति / Symmetry about the (x)-axis
D कोई ग्राफ नहीं / No graph
Explanation opens after your attempt
Correct Answer
A. मूल बिंदु के सापेक्ष सममिति / Symmetry about the origin
Step 1
Concept
(f(-x)=(-x)5 =-x-5 =-f(x)). Therefore it is an odd function.
Step 2
Why this answer is correct
The correct answer is A. मूल बिंदु के सापेक्ष सममिति / Symmetry about the origin. (f(-x)=(-x)5 =-x-5 =-f(x)). Therefore it is an odd function.
Step 3
Exam Tip
(f(-x)=(-x)5 =-x-5 =-f(x)) है। इसलिए यह विषम फलन है।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=x-6 ) के ग्राफ की सममिति कौन सी है?
What is the symmetry of the graph of (f(x)=x-6 )?
#graphs
#power-function
#symmetry
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (y)-अक्ष के सापेक्ष सममिति / Symmetry about the (y)-axis
B मूल बिंदु के सापेक्ष सममिति / Symmetry about the origin
C (x)-अक्ष के सापेक्ष सममिति / Symmetry about the (x)-axis
D कोई सममिति नहीं / No symmetry
Explanation opens after your attempt
Correct Answer
A. (y)-अक्ष के सापेक्ष सममिति / Symmetry about the (y)-axis
Step 1
Concept
(f(-x)=(-x)6 =x-6 =f(x)). Therefore it is an even function.
Step 2
Why this answer is correct
The correct answer is A. (y)-अक्ष के सापेक्ष सममिति / Symmetry about the (y)-axis. (f(-x)=(-x)6 =x-6 =f(x)). Therefore it is an even function.
Step 3
Exam Tip
(f(-x)=(-x)6 =x-6 =f(x)) है। इसलिए यह सम फलन है।
Login to save your score, XP, coins and progress. Login
महत्तम पूर्णांक फलन (f(x)=\lfloor x \rfloor) में (f(-2.3)) का मान क्या है?
For the greatest integer function (f(x)=\lfloor x \rfloor), what is (f(-2.3))?
#graphs
#greatest-integer
#value
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (-3)
B (-2)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
\(\lfloor x \rfloor\) gives the greatest integer less than or equal to (x). For (-2.3), that integer is (-3).
Step 2
Why this answer is correct
The correct answer is A. (-3). \(\lfloor x \rfloor\) gives the greatest integer less than or equal to (x). For (-2.3), that integer is (-3).
Step 3
Exam Tip
\(\lfloor x \rfloor\) (x) से कम या बराबर सबसे बड़ा पूर्णांक देता है। (-2.3) के लिए वह (-3) है।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=\lfloor x \rfloor) के ग्राफ में अंतराल \(2\le x<3\) पर मान क्या है?
What is the value of (f(x)=\lfloor x \rfloor) on the interval \(2\le x<3\)?
#graphs
#greatest-integer
#step
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (2)
B (3)
C (x)
D (0)
Explanation opens after your attempt
Step 1
Concept
On \(2\le x<3\), the greatest integer remains (2). Hence the graph is horizontal on this interval.
Step 2
Why this answer is correct
The correct answer is A. (2). On \(2\le x<3\), the greatest integer remains (2). Hence the graph is horizontal on this interval.
Step 3
Exam Tip
\(2\le x<3\) पर सबसे बड़ा पूर्णांक (2) ही रहता है। इसलिए ग्राफ इस अंतराल पर क्षैतिज है।
Login to save your score, XP, coins and progress. Login
फलन (g(x)=\lceil x \rceil) में (g(4.1)) का मान क्या है?
What is (g(4.1)) for the function (g(x)=\lceil x \rceil)?
#graphs
#ceiling-function
#value
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (5)
B (4)
C (4.1)
D (0)
Explanation opens after your attempt
Step 1
Concept
\(\lceil x \rceil\) gives the smallest integer greater than or equal to (x). For (4.1), it is (5).
Step 2
Why this answer is correct
The correct answer is A. (5). \(\lceil x \rceil\) gives the smallest integer greater than or equal to (x). For (4.1), it is (5).
Step 3
Exam Tip
\(\lceil x \rceil\) (x) से बड़ा या बराबर सबसे छोटा पूर्णांक देता है। (4.1) के लिए यह (5) है।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=\operatorname{sgn}(x+3)) में (x=-3) पर मान क्या है?
What is the value of (f(x)=\operatorname{sgn}(x+3)) at (x=-3)?
#graphs
#signum
#value
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (0)
B (-1)
C (1)
D (3)
Explanation opens after your attempt
Step 1
Concept
At (x=-3), (x+3=0). The signum function gives (0) at (0).
Step 2
Why this answer is correct
The correct answer is A. (0). At (x=-3), (x+3=0). The signum function gives (0) at (0).
Step 3
Exam Tip
(x=-3) पर (x+3=0) होता है। साइनम फलन (0) पर (0) देता है।
Login to save your score, XP, coins and progress. Login
फलन (f(x)=\operatorname{sgn}(2x-8)) के ग्राफ में छलांग किस (x) पर होगी?
At which (x) will the graph of (f(x)=\operatorname{sgn}(2x-8)) have a jump?
#graphs
#signum
#jump
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (x=4)
B (x=-4)
C (x=8)
D (x=2)
Explanation opens after your attempt
Step 1
Concept
A signum graph changes when the inside expression is zero. From (2x-8=0), we get (x=4).
Step 2
Why this answer is correct
The correct answer is A. (x=4). A signum graph changes when the inside expression is zero. From (2x-8=0), we get (x=4).
Step 3
Exam Tip
साइनम ग्राफ अंदर की अभिव्यक्ति शून्य होने पर बदलता है। (2x-8=0) से (x=4) मिलता है।
Login to save your score, XP, coins and progress. Login
फलन (y=\min(x,4)) के ग्राफ में (x>4) के लिए (y) क्या है?
For (x>4), what is (y) in the graph of (y=\min(x,4))?
#graphs
#piecewise
#minimum
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (y=4)
B (y=x)
C (y=-4)
D (y=x-4)
Explanation opens after your attempt
Step 1
Concept
When (x>4), the smaller value between (x) and (4) is (4). Hence the graph is constant at (y=4).
Step 2
Why this answer is correct
The correct answer is A. (y=4). When (x>4), the smaller value between (x) and (4) is (4). Hence the graph is constant at (y=4).
Step 3
Exam Tip
जब (x>4) हो तो (x) और (4) में छोटा मान (4) है। इसलिए ग्राफ (y=4) पर स्थिर है।
Login to save your score, XP, coins and progress. Login
फलन (y=|x-3|-(x-3)) में \(x\ge 3\) के लिए (y) क्या होगा?
For \(x\ge 3\), what is (y) in (y=|x-3|-(x-3))?
#graphs
#modulus
#piecewise
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (0)
B (2x-6)
C (6-2x)
D (x-3)
Explanation opens after your attempt
Step 1
Concept
For \(x\ge 3\), (|x-3|=x-3). Hence (y=(x-3)-(x-3)=0).
Step 2
Why this answer is correct
The correct answer is A. (0). For \(x\ge 3\), (|x-3|=x-3). Hence (y=(x-3)-(x-3)=0).
Step 3
Exam Tip
\(x\ge 3\) पर (|x-3|=x-3) है। इसलिए (y=(x-3)-(x-3)=0) मिलता है।
Login to save your score, XP, coins and progress. Login
ग्राफ \(y=x^2\) और (y=6-x) किस (x) मानों पर प्रतिच्छेद करते हैं?
At which (x) values do the graphs \(y=x^2\) and (y=6-x) intersect?
#graphs
#intersection
#quadratic
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (x=-3,2)
B (x=3,-2)
C (x=1,6)
D (x=0,6)
Explanation opens after your attempt
Correct Answer
A. (x=-3,2)
Step 1
Concept
For intersection, set \(x^2=6-x\). From \(x^2+x-6=0\), we get (x=-3,2).
Step 2
Why this answer is correct
The correct answer is A. (x=-3,2). For intersection, set \(x^2=6-x\). From \(x^2+x-6=0\), we get (x=-3,2).
Step 3
Exam Tip
प्रतिच्छेद के लिए \(x^2=6-x\) रखें। \(x^2+x-6=0\) से (x=-3,2) मिलते हैं।
Login to save your score, XP, coins and progress. Login
ग्राफ (y=|x+1|) और (y=5) किन (x) मानों पर मिलते हैं?
At which (x) values do the graphs (y=|x+1|) and (y=5) meet?
#graphs
#intersection
#modulus
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (x=-6,4)
B (x=-5,5)
C (x=1,5)
D (x=-4,6)
Explanation opens after your attempt
Correct Answer
A. (x=-6,4)
Step 1
Concept
From (|x+1|=5), we get \(x+1=\pm5\). Therefore (x=-6) or (x=4).
Step 2
Why this answer is correct
The correct answer is A. (x=-6,4). From (|x+1|=5), we get \(x+1=\pm5\). Therefore (x=-6) or (x=4).
Step 3
Exam Tip
(|x+1|=5) से \(x+1=\pm5\) मिलता है। इसलिए (x=-6) या (x=4) है।
Login to save your score, XP, coins and progress. Login
ग्राफ \(y=\sqrt{x}\) और (y=x-2) के प्रतिच्छेद के लिए सही (x) मान कौन सा है?
Which (x) value is correct for the intersection of \(y=\sqrt{x}\) and (y=x-2)?
#graphs
#intersection
#square-root
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (x=4)
B (x=1)
C (x=2)
D (x=0)
Explanation opens after your attempt
Step 1
Concept
In \(\sqrt{x}=x-2\), the right side requires \(x\ge 2\). At (x=4), both sides are (2).
Step 2
Why this answer is correct
The correct answer is A. (x=4). In \(\sqrt{x}=x-2\), the right side requires \(x\ge 2\). At (x=4), both sides are (2).
Step 3
Exam Tip
\(\sqrt{x}=x-2\) में दायां पक्ष \(x\ge 2\) मांगता है। (x=4) रखने पर दोनों मान (2) हैं।
Login to save your score, XP, coins and progress. Login
ग्राफ \(y=\frac{1}{x}\) और (y=x) किन बिंदुओं पर मिलते हैं?
At which points do the graphs \(y=\frac{1}{x}\) and (y=x) meet?
#graphs
#intersection
#rational
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A ((1,1)) और ((-1,-1)) / ((1,1)) and ((-1,-1))
B ((0,0)) और ((1,1)) / ((0,0)) and ((1,1))
C ((1,-1)) और ((-1,1)) / ((1,-1)) and ((-1,1))
D ((2,2)) और ((-2,-2)) / ((2,2)) and ((-2,-2))
Explanation opens after your attempt
Correct Answer
A. ((1,1)) और ((-1,-1)) / ((1,1)) and ((-1,-1))
Step 1
Concept
From \(\frac{1}{x}=x\), we get \(x^2=1\). Hence \(x=\pm1\) and the points are ((1,1)), ((-1,-1)).
Step 2
Why this answer is correct
The correct answer is A. ((1,1)) और ((-1,-1)) / ((1,1)) and ((-1,-1)). From \(\frac{1}{x}=x\), we get \(x^2=1\). Hence \(x=\pm1\) and the points are ((1,1)), ((-1,-1)).
Step 3
Exam Tip
\(\frac{1}{x}=x\) से \(x^2=1\) मिलता है। इसलिए \(x=\pm1\) और बिंदु ((1,1)), ((-1,-1)) हैं।
Login to save your score, XP, coins and progress. Login
फलन (y=f(x-3)+2) का ग्राफ (y=f(x)) से कैसे प्राप्त होगा?
How is the graph (y=f(x-3)+2) obtained from (y=f(x))?
#graphs
#transformation
#shift
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (3) इकाई दाईं ओर और (2) इकाई ऊपर / (3) units right and (2) units up
B (3) इकाई बाईं ओर और (2) इकाई ऊपर / (3) units left and (2) units up
C (3) इकाई दाईं ओर और (2) इकाई नीचे / (3) units right and (2) units down
D (2) इकाई दाईं ओर और (3) इकाई ऊपर / (2) units right and (3) units up
Explanation opens after your attempt
Correct Answer
A. (3) इकाई दाईं ओर और (2) इकाई ऊपर / (3) units right and (2) units up
Step 1
Concept
The term (x-3) shifts the graph (3) units right horizontally. The outside (+2) moves it (2) units up.
Step 2
Why this answer is correct
The correct answer is A. (3) इकाई दाईं ओर और (2) इकाई ऊपर / (3) units right and (2) units up. The term (x-3) shifts the graph (3) units right horizontally. The outside (+2) moves it (2) units up.
Step 3
Exam Tip
(x-3) क्षैतिज रूप से (3) इकाई दाईं ओर खिसकाता है। बाहर (+2) ग्राफ को (2) इकाई ऊपर ले जाता है।
Login to save your score, XP, coins and progress. Login
फलन (y=-f(x)+4) में (y=f(x)) के ग्राफ पर कौन सा परिवर्तन होगा?
What transformation happens to the graph of (y=f(x)) in (y=-f(x)+4)?
#graphs
#transformation
#reflection
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (x)-अक्ष में परावर्तन और (4) इकाई ऊपर / Reflection in the (x)-axis and (4) units up
B (y)-अक्ष में परावर्तन और (4) इकाई ऊपर / Reflection in the (y)-axis and (4) units up
C (x)-अक्ष में परावर्तन और (4) इकाई दाईं ओर / Reflection in the (x)-axis and (4) units right
D केवल (4) इकाई नीचे / Only (4) units down
Explanation opens after your attempt
Correct Answer
A. (x)-अक्ष में परावर्तन और (4) इकाई ऊपर / Reflection in the (x)-axis and (4) units up
Step 1
Concept
(-f(x)) gives reflection in the (x)-axis. Then (+4) shifts the graph upward.
Step 2
Why this answer is correct
The correct answer is A. (x)-अक्ष में परावर्तन और (4) इकाई ऊपर / Reflection in the (x)-axis and (4) units up. (-f(x)) gives reflection in the (x)-axis. Then (+4) shifts the graph upward.
Step 3
Exam Tip
(-f(x)) (x)-अक्ष में परावर्तन देता है। फिर (+4) ग्राफ को ऊपर खिसकाता है।
Login to save your score, XP, coins and progress. Login
फलन (y=f(-x-2)) को (y=f(x)) से समझने के लिए अंदर की अभिव्यक्ति किस रूप में लिखी जा सकती है?
To understand (y=f(-x-2)) from (y=f(x)), how can the inside expression be written?
#graphs
#transformation
#reflection
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (f(-(x+2)))
B (f(x-2))
C (f(x+2))
D (f(-(x-2)))
Explanation opens after your attempt
Correct Answer
A. (f(-(x+2)))
Step 1
Concept
(-x-2=-(x+2)). It is easier to read the graph as a reflection in the (y)-axis with a horizontal shift.
Step 2
Why this answer is correct
The correct answer is A. (f(-(x+2))). (-x-2=-(x+2)). It is easier to read the graph as a reflection in the (y)-axis with a horizontal shift.
Step 3
Exam Tip
(-x-2=-(x+2)) है। पहले (y)-अक्ष में परावर्तन और फिर क्षैतिज खिसकाव समझना आसान होता है।
Login to save your score, XP, coins and progress. Login
फलन (y=|f(x)|) का ग्राफ (y=f(x)) से बनाते समय ऋणात्मक (y)-मानों का क्या होता है?
When drawing (y=|f(x)|) from (y=f(x)), what happens to negative (y)-values?
#graphs
#transformation
#absolute-value
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A वे (x)-अक्ष के ऊपर परावर्तित होते हैं / They are reflected above the (x)-axis
B वे (y)-अक्ष के बाईं ओर जाते हैं / They move to the left of the (y)-axis
C वे हट जाते हैं / They disappear
D वे (0) हो जाते हैं / They become (0)
Explanation opens after your attempt
Correct Answer
A. वे (x)-अक्ष के ऊपर परावर्तित होते हैं / They are reflected above the (x)-axis
Step 1
Concept
With modulus outside, all (y)-values become non-negative. Hence the part below the (x)-axis reflects upward.
Step 2
Why this answer is correct
The correct answer is A. वे (x)-अक्ष के ऊपर परावर्तित होते हैं / They are reflected above the (x)-axis. With modulus outside, all (y)-values become non-negative. Hence the part below the (x)-axis reflects upward.
Step 3
Exam Tip
मापांक बाहर होने से सभी (y)-मान अऋणात्मक हो जाते हैं। इसलिए (x)-अक्ष के नीचे वाला भाग ऊपर परावर्तित होता है।
Login to save your score, XP, coins and progress. Login
फलन (y=f(|x|)) का ग्राफ (y=f(x)) से बनाते समय कौन सा भाग दोहराया जाता है?
When drawing (y=f(|x|)) from (y=f(x)), which part is repeated?
#graphs
#transformation
#absolute-input
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A दाईं ओर का भाग (y)-अक्ष में परावर्तित होता है / The right-side part is reflected in the (y)-axis
B बाईं ओर का भाग (x)-अक्ष में परावर्तित होता है / The left-side part is reflected in the (x)-axis
C पूरा ग्राफ नीचे खिसकता है / The whole graph shifts downward
D पूरा ग्राफ (x)-अक्ष में परावर्तित होता है / The whole graph reflects in the (x)-axis
Explanation opens after your attempt
Correct Answer
A. दाईं ओर का भाग (y)-अक्ष में परावर्तित होता है / The right-side part is reflected in the (y)-axis
Step 1
Concept
Because of (|x|), even for (x<0), the input to (f) is positive. Hence the right-side graph reflects to the left.
Step 2
Why this answer is correct
The correct answer is A. दाईं ओर का भाग (y)-अक्ष में परावर्तित होता है / The right-side part is reflected in the (y)-axis. Because of (|x|), even for (x<0), the input to (f) is positive. Hence the right-side graph reflects to the left.
Step 3
Exam Tip
(|x|) के कारण (x<0) पर भी (f) में धनात्मक इनपुट जाता है। इसलिए दाईं ओर का ग्राफ बाईं ओर परावर्तित होता है।
Login to save your score, XP, coins and progress. Login
