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

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

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

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

• [-5, 5] by [-10, 20]

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 $x=a$.

Each Exercise gives a formula for a function y = f(x). In each case, find $f^{-1}(x)$ and identify the domain and range of $f^{-1}.$ As a check, show that $f\left(f^{-1}(x)\right)=f^{-1}(f(x))=x.$ $f(x)=1 / x^{2}, \quad x>0$

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]

Find the function values.

$$\sin ^2 \frac{\pi}{8}$$

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]

Find the domain and range of each function.

$$g(z)=\sqrt{4-z^2}$$

What is a piecewise-defined function? Give examples.

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.

Find an appropriate graphing software viewing window for the given function and use it to display its graph. The window should give a picture of the overall behavior of the function. There is more than one choice, but incorrect choices can miss important aspects of the function. $y=x+\frac{1}{10} \sin 30 x$

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

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