If (f:\mathbb{R}\to\mathbb{R}) and (f(x)=|x+5|+|x-2|), what is the range?

Correct answer: ([7,\infty))

The direct answer is option A: [7,∞). The expression is f(x)=|x+5|+|x−2|. Absolute value means distance on the number line: |x+5| is the distance from x to −5, and |x−2| is the distance from x to 2. The distance between −5 and 2 is 7. For every x between −5 and 2, the two distances add to exactly 7. Outside that interval, moving farther away increases the total distance, so values larger than 7 occur. Thus the minimum is 7 and the range is [7,∞). Option A is correct because 7 is included and every larger value is possible. Option B, [0,∞), wrongly assumes the sum can be zero; both distances cannot be zero because x cannot equal −5 and 2 simultaneously. Option C, {7}, includes only the minimum and ignores larger values outside the interval. Option D contains values below 7, which are impossible. The exam idea is that the sum of distances from a point to two fixed points is at least the distance between those points.