Problems

01

Compute difference quotient

Suppose $f(x)=-x^3$. Compute and simplify the difference quotient: $$\frac{f(a+h)-f(a)}{h}$$

Show your steps!

02

Domains of funny functions

Consider the following functions:

• (a) $f(x)=\sqrt{3-x}+\sqrt{4+x}$
• (b) $f(x)=\frac{x+1}{1+\frac{1}{1+x}}$

What is the largest possible domain for each of these functions?

Show your steps!

03

Piecewise function from graph

Find the piecewise formula for the function with this graph:

04

Even v Odd for a product function

• (a) Consider the function $f(x)=x|x|$. Is it even or odd?
• (b) If $f(x)$ is even/odd and $g(x)$ is even/odd, what is $f\cdot g$? (There are four separate cases to describe.)