Write the linear function $f$ such that it has the indicated function values. Then sketch the graph of the function.

$$f(0)=-5, f(4)=-8$$

The function $g$ is related to one of the common functions described on page 98. (d) Use function notation to write $g$ in terms of $f$.

$$g(x)=(x-1)^3+2$$

The function $g$ is related to one of the common functions described on page 98. $(c)$ Sketch the graph of $g$.

$$g(x)=(x-1)^3+2$$

Does the function have an inverse function?

$$\begin{array}{|l|l|l|l|l|l|l|} \hline x & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline f(x) & -2 & 1 & 2 & 1 & -2 & -6 \\ \hline \end{array}$$

Use the given value of $k$ to complete the table for the direct variation model

$$y=k x^2$$

Plot the points on a rectangular coordinate system.

$$\begin{array}{|l|l|l|l|l|l|} \hline x & 2 & 4 & 6 & 8 & 10 \\ \hline y=k x^2 & & & & & \\ \hline \end{array}$$

$$k=1$$

The function $g$ is related to one of the common functions described on page 98. (b) Describe the sequence of transformations from $f$ to $g$.

$$g(x)=(x-1)^3+2$$

Find the zeros of the function analytically.

$$f(x)=x^3-4 x^2-9 x+36$$

$g$ is related to one of the common functions described on page $98$. (a) Identify the common function $f$.

$$g(x)=(x-1)^3+2$$

Direct Variation $\quad$ Assume that $y$ is directly proportional to $x$. Use the given $x$-value and $\boldsymbol{y}$-value to find a linear model that relates $\boldsymbol{y}$ and $\boldsymbol{x}$.

$$x=5, y=12$$

Write the linear function $f$ such that it has the indicated function values. Then sketch the graph of the function.

$$f(2)=-6, f(-1)=3$$

Determine whether the equation represents $y$ as a function of $x$.

$$(x+2)^2+(y-1)^2=25$$

Graph the functions $f, g$, and $f+g$ on the same set of coordinate axes.

$$f(x)=4-x^2, \quad g(x)=x$$

Determine whether the equation represents $y$ as a function of $x$.

$$y^2=x^2-1$$

Determine whether the relation represents $y$ as a function of $x$.

$$\begin{array}{|l|l|l|l|l|l|} \hline \text { Input, } x & 0 & 1 & 2 & 1 & 0 \\ \hline \text { Output, } y & -4 & -2 & 0 & 2 & 4 \\ \hline \end{array}$$