Advanced MathHardMaximum of an absolute-value function
Advanced Math practice question
The function h is defined by h(x) = 5 − |x − 1|. What is the maximum value of h(x)?
- A. 5Correct
- B. 1
- C. 6
- D. 4
Answer: A. 5
|x − 1| is never negative and equals 0 when x = 1. So h(x) is at most 5 − 0 = 5, reached at x = 1.
Why the other answers are wrong
- B. 1
- 1 is the x-value where the maximum occurs, not the maximum value.
- C. 6
- 6 would need |x − 1| = −1, which is impossible.
- D. 4
- 4 is h(0) or h(2), one unit away from the peak.
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