Find the domain. $y=-1+\sqrt[3]{2-x}$

Use a graphing calculator or computer to determine if the given viewing windows display is the appropriate graph of the specified function.

$$f(x)=x^3-4 x^2-4 x+16$$

• [-20, 20] by [-100, 100]

You want to make an $80^{\circ}$ angle by marking an arc on the perimeter of a 12-in.-diameter disk and drawing lines from the ends of the arc to the disk’s center. To the nearest tenth of an inch, how long should the arc be?

Say whether the function is even, odd, or neither. Give reasons for your answer.

$g(x)=\frac{x}{x^2-1}$

Let $f(x)=2 x+3$ and let $\epsilon>0$ be any positive number. Prove that $|f(x)-f(0)|<\epsilon$ whenever $|x-0|<\frac{\epsilon}{2}$. Here the notation $f(a)$ means the value of the expression $2 x+3$ when $x=a$.

Use a graphing calculator or computer to determine if the given viewing windows display is the appropriate graph of the specified function.

$$f(x)=x^3-4 x^2-4 x+16$$

• [-5, 5] by [-10, 20]

Graph the circles whose equations are given. Label each circle's center and intercepts (if any) with their coordinate pairs.

$$x^2+y^2-4 x-(9 / 4)=0$$

Use a graphing calculator or computer to determine if the given viewing windows display is the appropriate graph of the specified function.

$$f(x)=x^3-4 x^2-4 x+16$$

• [-3, 3] by [-10, 10]

What is a piecewise-defined function? Give examples.

Use graphs to find approximate solutions. $3-2^{-x}=0$

Use graphing software to determine which of the given viewing windows displays the most appropriate graph of the specified function. $f(x)=x^{3}-4 x^{2}-4 x+16$ a. [-1, 1] by [-5, 5] b. [-3, 3] by [-10, 10] c. [-5, 5] by [-10, 20] d. [-20, 20] by [-100, 100]

How does $f(x)=\log _{x}(2)$ compare with $g(x)=\log _{2}(x) ?$ Here is one way to find out. a. Use the equation $\log _{a} b=(\ln b) /(\ln a)$ to express f(x) and g(x) in terms of natural logarithms. b. Graph f and g together. Comment on the behavior of f in relation to the signs and values of g.

Solve the equations or inequalities.

$$|x+1|=7$$

How are absolute values used to describe intervals or unions of intervals? Give examples.