# Suppose f is a function deﬁned

Suppose f is a function deﬁned for all real numbers which has amaximum value of 5 and a minimum value of −7. Label each of thefollowing as MUST, MIGHT, or NEVER true. Explain, and if you saymight, give an example of yes and an example of no.

A The maximum value of f(|x|) is 7.

B The maximum value of f(|x|) is 5.

C The maximum value of f(|x|) is 0.

D The minimum value of f(|x|) is 7.

E The minimum value of f(|x|) is 5.

F The minimum value of f(|x|) is 0.

G The maximum value of |f(x)| is 7.

H The maximum value of |f(x)| is 5.

I The maximum value of |f(x)| is 0.

J The minimum value of |f(x)| is 7.

K The minimum value of |f(x)| is 5.

L The minimum value of |f(x)| is 0.

Now suppose f is a continuous function deﬁned for all realnumbers which has a maximum value of 5 and a minimum value of −7.Which of the answers above stay the same (why?), and which change(to what, and why?)

(A) NEVER

(B) MIGHT

(C) MIGHT

(D) NEVER

(E) MIGHT

(F) MIGHT

(G) ALWAYS

(H) NEVER

(I) NEVER

(J) NEVER

(K) MIGHT

(L) MIGHT

All of the above answers remain the same as each of theabove examples can be redefined using intervals so that f(x)becomes continuous.

For example, the last function in (L) can be redefinedas

The properties will remain the same.

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