# 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?)

Answer:

**(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.**