फलन (f(x)=|2x-8|+3) का शीर्ष कौन सा है?
What is the vertex of (f(x)=|2x-8|+3)?
#standard-functions
#modulus-graph
#vertex-linear-inside
A ((4,3))
B ((-4,3))
C ((8,3))
D ((4,-3))
Explanation opens after your attempt
Correct Answer
A. ((4,3))
Step 1
Concept
For the vertex, set (2x-8=0), which gives (x=4). The outside (+3) makes the vertex ((4,3)).
Step 2
Why this answer is correct
The correct answer is A. ((4,3)). For the vertex, set (2x-8=0), which gives (x=4). The outside (+3) makes the vertex ((4,3)).
Step 3
Exam Tip
शीर्ष के लिए (2x-8=0) रखें जिससे (x=4) मिलता है। बाहर (+3) होने से शीर्ष ((4,3)) है।
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फलन (f(x)=|x+4|-|x-2|) का (x=-1) पर मान क्या है?
What is the value of (f(x)=|x+4|-|x-2|) at (x=-1)?
#standard-functions
#modulus-graph
#value
A (0)
B (6)
C (-6)
D (3)
Explanation opens after your attempt
Step 1
Concept
(f(-1)=|3|-|-3|=3-3=0). Take the modulus values before subtracting.
Step 2
Why this answer is correct
The correct answer is A. (0). (f(-1)=|3|-|-3|=3-3=0). Take the modulus values before subtracting.
Step 3
Exam Tip
(f(-1)=|3|-|-3|=3-3=0)। चिन्ह बदलने से पहले मापांक का मान लें।
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फलन (f(x)=|x-2|+|x-6|) का (x=4) पर मान क्या है?
What is the value of (f(x)=|x-2|+|x-6|) at (x=4)?
#standard-functions
#modulus-graph
#evaluation
A (4)
B (2)
C (6)
D (0)
Explanation opens after your attempt
Step 1
Concept
(f(4)=|2|+|-2|=2+2=4). Evaluate both modulus parts separately.
Step 2
Why this answer is correct
The correct answer is A. (4). (f(4)=|2|+|-2|=2+2=4). Evaluate both modulus parts separately.
Step 3
Exam Tip
(f(4)=|2|+|-2|=2+2=4)। मापांक के दोनों भाग अलग से निकालें।
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फलन (f(x)=-|x-1|+4) का अधिकतम मान क्या है?
What is the maximum value of (f(x)=-|x-1|+4)?
#standard-functions
#modulus-graph
#maximum
A (4)
B (1)
C (0)
D (-4)
Explanation opens after your attempt
Step 1
Concept
Since \(|x-1|\ge 0\), \(-|x-1|+4\le 4\). The maximum value (4) occurs at (x=1).
Step 2
Why this answer is correct
The correct answer is A. (4). Since \(|x-1|\ge 0\), \(-|x-1|+4\le 4\). The maximum value (4) occurs at (x=1).
Step 3
Exam Tip
क्योंकि \(|x-1|\ge 0\), इसलिए \(-|x-1|+4\le 4\)। अधिकतम मान (4) (x=1) पर मिलता है।
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फलन (f(x)=2|x+2|-6) के (x)-अक्ष प्रतिच्छेद कौन से हैं?
What are the (x)-intercepts of (f(x)=2|x+2|-6)?
#standard-functions
#modulus-graph
#x-intercepts
A (x=1) और (x=-5) / (x=1) and (x=-5)
B (x=3) और (x=-3) / (x=3) and (x=-3)
C (x=2) और (x=-6) / (x=2) and (x=-6)
D (x=0) और (x=-4) / (x=0) and (x=-4)
Explanation opens after your attempt
Correct Answer
A. (x=1) और (x=-5) / (x=1) and (x=-5)
Step 1
Concept
From (2|x+2|-6=0), we get (|x+2|=3). So (x=1) and (x=-5).
Step 2
Why this answer is correct
The correct answer is A. (x=1) और (x=-5) / (x=1) and (x=-5). From (2|x+2|-6=0), we get (|x+2|=3). So (x=1) and (x=-5).
Step 3
Exam Tip
(2|x+2|-6=0) से (|x+2|=3) मिलता है। इसलिए (x=1) और (x=-5) हैं।
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फलन (f(x)=|3x-9|) का शीर्ष किस (x) मान पर है?
At which (x)-value is the vertex of (f(x)=|3x-9|)?
#standard-functions
#modulus-graph
#inside-zero
A (x=3)
B (x=9)
C (x=-3)
D (x=0)
Explanation opens after your attempt
Step 1
Concept
The vertex occurs when (3x-9=0). This gives (x=3).
Step 2
Why this answer is correct
The correct answer is A. (x=3). The vertex occurs when (3x-9=0). This gives (x=3).
Step 3
Exam Tip
शीर्ष तब मिलता है जब (3x-9=0)। इससे (x=3) मिलता है।
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फलन (f(x)=|2x+4|+1) का न्यूनतम मान क्या है?
What is the minimum value of (f(x)=|2x+4|+1)?
#standard-functions
#modulus-graph
#minimum
A (1)
B (0)
C (2)
D (-1)
Explanation opens after your attempt
Step 1
Concept
The minimum value of a modulus is (0). Therefore the minimum value of (|2x+4|+1) is (1).
Step 2
Why this answer is correct
The correct answer is A. (1). The minimum value of a modulus is (0). Therefore the minimum value of (|2x+4|+1) is (1).
Step 3
Exam Tip
मापांक का न्यूनतम मान (0) होता है। इसलिए (|2x+4|+1) का न्यूनतम मान (1) है।
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फलन (f(x)=|x-5|-2) के आलेख का शीर्ष कौन सा है?
What is the vertex of the graph of (f(x)=|x-5|-2)?
#standard-functions
#modulus-graph
#vertex
A ((5,-2))
B ((-5,-2))
C ((5,2))
D ((-2,5))
Explanation opens after your attempt
Correct Answer
A. ((5,-2))
Step 1
Concept
(|x-5|) becomes zero at (x=5), and (-2) is added outside. So the vertex is ((5,-2)).
Step 2
Why this answer is correct
The correct answer is A. ((5,-2)). (|x-5|) becomes zero at (x=5), and (-2) is added outside. So the vertex is ((5,-2)).
Step 3
Exam Tip
(|x-5|) शून्य (x=5) पर होता है और बाहर (-2) जुड़ता है। इसलिए शीर्ष ((5,-2)) है।
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फलन (f(x)=|x-1|-|x+3|) में (x=2) पर मान क्या है?
What is the value of (f(x)=|x-1|-|x+3|) at (x=2)?
#standard-functions
#modulus-graph
#evaluation
A (-4)
B (4)
C (2)
D (0)
Explanation opens after your attempt
Step 1
Concept
(f(2)=|1|-|5|=1-5=-4). Evaluate each modulus part separately.
Step 2
Why this answer is correct
The correct answer is A. (-4). (f(2)=|1|-|5|=1-5=-4). Evaluate each modulus part separately.
Step 3
Exam Tip
(f(2)=|1|-|5|=1-5=-4)। मापांक वाले प्रत्येक भाग का मान अलग निकालें।
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फलन (f(x)=|x-2|+|x+2|) का (x=1) पर मान क्या है?
What is the value of (f(x)=|x-2|+|x+2|) at (x=1)?
#standard-functions
#modulus-graph
#evaluation
A (4)
B (2)
C (6)
D (0)
Explanation opens after your attempt
Step 1
Concept
(f(1)=|-1|+|3|=1+3=4). In modulus questions, evaluate each part separately.
Step 2
Why this answer is correct
The correct answer is A. (4). (f(1)=|-1|+|3|=1+3=4). In modulus questions, evaluate each part separately.
Step 3
Exam Tip
(f(1)=|-1|+|3|=1+3=4)। मापांक वाले प्रश्नों में हर भाग अलग से निकालें।
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फलन (f(x)=|x-2 -4|) के शून्यक कौन से हैं?
What are the zeros of (f(x)=|x-2 -4|)?
#standard-functions
#modulus-graph
#zeros
A (x=2) और (x=-2) / (x=2) and (x=-2)
B (x=4) और (x=-4) / (x=4) and (x=-4)
C केवल (x=0) / Only (x=0)
D कोई शून्यक नहीं / No zero
Explanation opens after your attempt
Correct Answer
A. (x=2) और (x=-2) / (x=2) and (x=-2)
Step 1
Concept
A modulus is zero only when the inside expression is zero. From \(x^2-4=0\), we get \(x=\pm 2\).
Step 2
Why this answer is correct
The correct answer is A. (x=2) और (x=-2) / (x=2) and (x=-2). A modulus is zero only when the inside expression is zero. From \(x^2-4=0\), we get \(x=\pm 2\).
Step 3
Exam Tip
मापांक शून्य तभी होता है जब अंदर की राशि शून्य हो। \(x^2-4=0\) से \(x=\pm 2\) मिलता है।
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फलन (f(x)=|x-1|+|x+1|) में (x=0) पर मान क्या है?
What is the value of (f(x)=|x-1|+|x+1|) at (x=0)?
#standard-functions
#modulus-graph
#evaluation
A (2)
B (0)
C (1)
D (-2)
Explanation opens after your attempt
Step 1
Concept
(f(0)=|-1|+|1|=1+1=2). Modulus always gives a non-negative value.
Step 2
Why this answer is correct
The correct answer is A. (2). (f(0)=|-1|+|1|=1+1=2). Modulus always gives a non-negative value.
Step 3
Exam Tip
(f(0)=|-1|+|1|=1+1=2)। मापांक हमेशा गैरऋणात्मक मान देता है।
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फलन (f(x)=|x|-|x-2|) का (x=3) पर मान क्या है?
What is the value of (f(x)=|x|-|x-2|) at (x=3)?
#standard-functions
#modulus-graph
#value
A (2)
B (4)
C (0)
D (-2)
Explanation opens after your attempt
Step 1
Concept
(f(3)=|3|-|1|=3-1=2). In modulus questions, substitute the inside values first.
Step 2
Why this answer is correct
The correct answer is A. (2). (f(3)=|3|-|1|=3-1=2). In modulus questions, substitute the inside values first.
Step 3
Exam Tip
(f(3)=|3|-|1|=3-1=2)। मापांक में पहले अंदर का मान लगाएं।
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फलन (f(x)=3|x-2|) का आलेख (y=|x-2|) की तुलना में कैसा है?
How is the graph of (f(x)=3|x-2|) compared with (y=|x-2|)?
#standard-functions
#modulus-graph
#vertical-stretch
A ऊर्ध्व रूप से खिंचा / Vertically stretched
B ऊर्ध्व रूप से दबा / Vertically compressed
C (3) इकाई दाईं ओर / Shifted (3) units right
D (3) इकाई नीचे / Shifted (3) units down
Explanation opens after your attempt
Correct Answer
A. ऊर्ध्व रूप से खिंचा / Vertically stretched
Step 1
Concept
The coefficient (3) multiplies every (y)-value by (3). So the graph is vertically stretched.
Step 2
Why this answer is correct
The correct answer is A. ऊर्ध्व रूप से खिंचा / Vertically stretched. The coefficient (3) multiplies every (y)-value by (3). So the graph is vertically stretched.
Step 3
Exam Tip
गुणांक (3) हर (y)-मान को (3) गुना करता है। इसलिए आलेख ऊर्ध्व रूप से खिंचता है।
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फलन (f(x)=|x+1|-4) के (x)-अक्ष प्रतिच्छेद कौन से हैं?
What are the (x)-intercepts of (f(x)=|x+1|-4)?
#standard-functions
#modulus-graph
#x-intercepts
A (x=3) और (x=-5) / (x=3) and (x=-5)
B (x=4) और (x=-4) / (x=4) and (x=-4)
C (x=1) और (x=-1) / (x=1) and (x=-1)
D (x=5) और (x=-3) / (x=5) and (x=-3)
Explanation opens after your attempt
Correct Answer
A. (x=3) और (x=-5) / (x=3) and (x=-5)
Step 1
Concept
On the (x)-axis, (|x+1|-4=0), so (|x+1|=4). This gives (x=3) and (x=-5).
Step 2
Why this answer is correct
The correct answer is A. (x=3) और (x=-5) / (x=3) and (x=-5). On the (x)-axis, (|x+1|-4=0), so (|x+1|=4). This gives (x=3) and (x=-5).
Step 3
Exam Tip
(x)-अक्ष पर (|x+1|-4=0), इसलिए (|x+1|=4)। इससे (x=3) और (x=-5) मिलते हैं।
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फलन (f(x)=|2x-6|) का न्यूनतम मान किस (x) पर मिलता है?
At which (x)-value does (f(x)=|2x-6|) attain its minimum value?
#standard-functions
#modulus-graph
#minimum-point
A (x=3)
B (x=6)
C (x=-3)
D (x=0)
Explanation opens after your attempt
Step 1
Concept
A modulus is minimum (0) when the inside expression is (0). From (2x-6=0), we get (x=3).
Step 2
Why this answer is correct
The correct answer is A. (x=3). A modulus is minimum (0) when the inside expression is (0). From (2x-6=0), we get (x=3).
Step 3
Exam Tip
मापांक का न्यूनतम मान (0) तब होता है जब अंदर की राशि (0) हो। (2x-6=0) से (x=3) मिलता है।
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फलन (f(x)=|x-3|+2) के आलेख का शीर्ष कौन सा है?
What is the vertex of the graph of (f(x)=|x-3|+2)?
#standard-functions
#modulus-graph
#vertex
A ((3,2))
B ((-3,2))
C ((3,-2))
D ((2,3))
Explanation opens after your attempt
Correct Answer
A. ((3,2))
Step 1
Concept
(|x-3|) becomes zero at (x=3), and (2) is added outside. So the vertex is ((3,2)).
Step 2
Why this answer is correct
The correct answer is A. ((3,2)). (|x-3|) becomes zero at (x=3), and (2) is added outside. So the vertex is ((3,2)).
Step 3
Exam Tip
(|x-3|) शून्य (x=3) पर होता है और बाहर (2) जुड़ता है। इसलिए शीर्ष ((3,2)) है।
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