Section 1
Graphs of Functions and Relations
Reading and Writing After reading this section, write out the answers to these questions. Use complete sentences.What is a linear function?
Reading and Writing After reading this section, write out the answers to these questions. Use complete sentences.What is a constant function?
Reading and Writing After reading this section, write out the answers to these questions. Use complete sentences.What is the graph of a constant function?
Reading and Writing After reading this section, write out the answers to these questions. Use complete sentences.What shape is the graph of an absolute value function?
Reading and Writing After reading this section, write out the answers to these questions. Use complete sentences.What is the graph of a quadratic function called?
Reading and Writing After reading this section, write out the answers to these questions. Use complete sentences.What is the identity function?
Graph each function and state its domain and range. See Examples 1 and 2$$h(x)=-2$$
Graph each function and state its domain and range. See Examples 1 and 2$$f(x)=4$$
Graph each function and state its domain and range. See Examples 1 and 2$$f(x)=2 x-1$$
Graph each function and state its domain and range. See Examples 1 and 2$$g(x)=x+2$$
Graph each function and state its domain and range. See Examples 1 and 2$$g(x)=\frac{1}{2} x+2$$
Graph each function and state its domain and range. See Examples 1 and 2$$h(x)=\frac{2}{3} x-4$$
Graph each function and state its domain and range. See Examples 1 and 2$$y=-\frac{2}{3} x+3$$
Graph each function and state its domain and range. See Examples 1 and 2$$y=-\frac{3}{4} x+4$$
Graph each function and state its domain and range. See Examples 1 and 2$$y=-0.3 x+6.5$$
Graph each function and state its domain and range. See Examples 1 and 2$$y=0.25 x-0.5$$
Graph each absolute value function and state its domain and range. See Examples 3 and 4$$f(x)=|x|+1$$
Graph each absolute value function and state its domain and range. See Examples 3 and 4$$g(x)=|x|-3$$
Graph each absolute value function and state its domain and range. See Examples 3 and 4$$h(x)=| x+1$$
Graph each absolute value function and state its domain and range. See Examples 3 and 4$$f(x)=|x-2|$$
Graph each absolute value function and state its domain and range. See Examples 3 and 4$$g(x)=| 3 x$$
Graph each absolute value function and state its domain and range. See Examples 3 and 4$$h(x)=|-2 x|$$
Graph each absolute value function and state its domain and range. See Examples 3 and 4$$f(x)=|2 x-1|$$
Graph each absolute value function and state its domain and range. See Examples 3 and 4$$y=| 2 x-3$$
Graph each absolute value function and state its domain and range. See Examples 3 and 4$$f(x)=|x-2|+1$$
Graph each absolute value function and state its domain and range. See Examples 3 and 4$$y=|x-1|+2$$
Graph each quadratic function and state its domain and range. See Example 5$$y=x^{2}$$
Graph each quadratic function and state its domain and range. See Example 5$$y=-x^{2}$$
Graph each quadratic function and state its domain and range. See Example 5$$g(x)=x^{2}+2$$
Graph each quadratic function and state its domain and range. See Example 5$$f(x)=x^{2}-4$$
Graph each quadratic function and state its domain and range. See Example 5$$f(x)=2 x^{2}$$
Graph each quadratic function and state its domain and range. See Example 5$$h(x)=-3 x^{2}$$
Graph each quadratic function and state its domain and range. See Example 5$$y=6-x^{2}$$
Graph each quadratic function and state its domain and range. See Example 5$$y=-2 x^{2}+3$$
Graph each square-root function and state its domain and range. See Example 6$$g(x)=2 \sqrt{x}$$
Graph each square-root function and state its domain and range. See Example 6$$g(x)=\sqrt{x}-1$$
Graph each square-root function and state its domain and range. See Example 6$$f(x)=\sqrt{x-1}$$
Graph each square-root function and state its domain and range. See Example 6$$f(x)=\sqrt{x+1}$$
Graph each square-root function and state its domain and range. See Example 6$$h(x)=-\sqrt{x}$$
Graph each square-root function and state its domain and range. See Example 6$$h(x)=-\sqrt{x-1}$$
Graph each square-root function and state its domain and range. See Example 6$$y=\sqrt{x}+2$$
Graph each square-root function and state its domain and range. See Example 6$$y=2 \sqrt{x}+1$$
Graph each piecewise function. See Example $7 .$
$f(x)=\left\{\begin{array}{ll}x & \text { for } x \geq 0 \\ -4 x & \text { for } x<0\end{array}\right.$
Graph each piecewise function. See Example $7 .$$$f(x)=\left\{\begin{array}{ll}3 x+1 & \text { for } x \geq 0 \\-x+1 & \text { for } x<0\end{array}\right.$$
Graph each piecewise function. See Example $7 .$$$f(x)=\left\{\begin{array}{ll}2 & \text { for } x>1 \\-2 & \text { for } x \leq 1\end{array}\right.$$
Graph each piecewise function. See Example $7 .$$$f(x)=\left\{\begin{array}{ll}3 & \text { for } x>-2 \\-4 & \text { for } x \leq-2\end{array}\right.$$
Graph each piecewise function. See Example $7 .$$$f(x)=\left\{\begin{array}{ll}\sqrt{x} & \text { for } x>1 \\x+3 & \text { for } x \leq 1\end{array}\right.$$
Graph each piecewise function. See Example 7 .$$f(x)=\left\{\begin{array}{ll}\sqrt{x-2} \text { for } x & \geq 3 \\6-x & \text { for } x<3\end{array}\right.$$
Graph each piecewise function. See Example 7 .$$f(x)=\left\{\begin{array}{ll}\sqrt{x} & \text { for } 0 \leq x \leq 4 \\x-4 & \text { for } x>4\end{array}\right.$$
Graph each piecewise function. See Example 7 .$$f(x)=\left\{\begin{array}{ll}\sqrt{x+1} & \text { for }-1 \leq x \leq 3 \\x-5 & \text { for } x>3\end{array}\right.$$
Graph each relation and state its domain and range. See Example $\mathcal{B}$$$x=|y|$$
Graph each relation and state its domain and range. See Example $\mathcal{B}$$$x=-|y|$$
Graph each relation and state its domain and range. See Example $\mathcal{B}$$$x=-y^{2}$$
Graph each relation and state its domain and range. See Example $\mathcal{B}$$$x=1-y^{2}$$
Graph each relation and state its domain and range. See Example $\mathcal{B}$$$x=5$$
Graph each relation and state its domain and range. See Example $\mathcal{B}$$$x=-3$$
Graph each relation and state its domain and range. See Example $\mathcal{B}$$$x+9=y^{2}$$
Graph each relation and state its domain and range. See Example $\mathcal{B}$$$x+3=|y|$$
Graph each relation and state its domain and range. See Example $\mathcal{B}$$$x=\sqrt{y}$$
Graph each relation and state its domain and range. See Example $\mathcal{B}$$$x=-\sqrt{y}$$
Graph each relation and state its domain and range. See Example $\mathcal{B}$$$x=(y-1)^{2}$$
Graph each function and state the domain and range.$$f(x)=1-|x|$$
Graph each relation and state its domain and range. See Example $\mathcal{B}$$$x=(y+2)^{2}$$
Graph each function and state the domain and range.$$h(x)=\sqrt{x-3}$$
Graph each function and state the domain and range.$$y=(x-3)^{2}-1$$
Graph each function and state the domain and range.$$y=x^{2}-2 x-3$$
Graph each function and state the domain and range.$$y=|x+3|+1$$
Graph each function and state the domain and range.$$f(x)=-2 x+4$$
Graph each function and state the domain and range.$$y=\sqrt{x}-3$$
Graph each function and state the domain and range.$$y=2|x|$$
Graph each function and state the domain and range.$$y=3 x-5$$
Graph each function and state the domain and range.$$g(x)=(x+2)^{2}$$
Graph each function and state the domain and range.$$y=-x^{2}+4 x-4$$
Graph each function and state the domain and range.$$y=-2|x-1|+4$$
Classify each function as either a linear, constant, quadratic, square-root, or absolute value function.$$f(x)=\sqrt{x-3}$$
Classify each function as either a linear, constant, quadratic, square-root, or absolute value function.$$f(x)=|x|+5$$
Classify each function as either a linear, constant, quadratic, square-root, or absolute value function.$$f(x)=4$$
Classify each function as either a linear, constant, quadratic, square-root, or absolute value function.$$f(x)=4 x-7$$
Classify each function as either a linear, constant, quadratic, square-root, or absolute value function.$$f(x)=4 x^{2}-7$$
Classify each function as either a linear, constant, quadratic, square-root, or absolute value function.$$f(x)=-3$$
Classify each function as either a linear, constant, quadratic, square-root, or absolute value function.$$f(x)=5+\sqrt{x}$$
Classify each function as either a linear, constant, quadratic, square-root, or absolute value function.$$f(x)=|x-99|$$
Classify each function as either a linear, constant, quadratic, square-root, or absolute value function.$$f(x)=99 x-100$$
Classify each function as either a linear, constant, quadratic, square-root, or absolute value function.$$f(x)=-5 x^{2}+8 x+2$$
Graph the function $f(x)=\sqrt{x^{2}}$ and explain what this graph illustrates.
Graph the function $f(x)=\frac{1}{x}$ and state the domain and range.
Graph $y=x^{2}, y=\frac{1}{2} x^{2},$ and $y=2 x^{2}$ on the same coordinate system. What can you say about the graph of $y=a x^{2}$ for $a>0 ?$
Graph $y=x^{2}, y=x^{2}+2,$ and $y=x^{2}-3$ on the same sereen. What can you say about the position of $y=x^{2}+k$ relative to $y=x^{2} ?$
Graph $y=x^{2}, y=(x+5)^{2},$ and $y=(x-2)^{2}$ on the same screen. What can you say about the position of $y=(x-h)^{2}$ relative to $y=x^{2} ?$
You can graph the relation $x=y^{2}$ by graphing the two functions $y=\sqrt{x}$ and $y=-\sqrt{x} .$ Try it and explain why this works.
Graph $y=(x-3)^{2}, y=|x-3|,$ and $y=\sqrt{x-3}$ on the same coordinate system. How does the graph of $y=f(x-h)$ compare to the graph of $y=f(x) ?$