In Exercises 15-20, sketch the graph of each function and determine whether the function has any absolute extreme values on its domain. Explain how your answer is consistent with Theorem 1. 16. y = 2 - x, -1 < x < 1 THEOREM 1-The Extreme Value Theorem If f is continuous on a closed interval [a, b], then f attains both an absolute maximum value M and an absolute minimum value m in [a, b]. That is, there are numbers x, and xz in [a, b] with f(x1) = m, f(x2) = M, and m s f(x) s M for every other x in [a, b].
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![In Exercises 15-20, sketch the graph of each function and determine
whether the function has any absolute extreme values on its domain.
Explain how your answer is consistent with Theorem 1.
16. y = 2 - x, -1 < x < 1
THEOREM 1-The Extreme Value Theorem
If f is continuous on a closed interval [a, b], then f attains both an absolute
maximum value M and an absolute minimum value m in [a, b]. That is, there are
numbers x, and xz in [a, b] with f(x1) = m, f(x2) = M, and m s f(x) s M for
every other x in [a, b].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ecf5e3e-b7b3-4ba9-b5d0-4ceff7990468%2F32c4aa96-62ca-4c2d-97b1-fd81e8f3fd44%2F0v12xh.png&w=3840&q=75)
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