The data can be described by the following mathematical models:

$$A=-0.9n +69$$

$$M= -0.3n +27.$$

a. Use the appropriate line graph to determine the percentage of seniors who used marijuana in $2005$.

b. Use the appropriate formula to determine the percentage of seniors who used marijuana in $2005$. Does the formula underestimate or overestimate the actual percentage displayed by the graph? By how much?

c. Use the appropriate line graph to estimate the percentage of seniors who used alcohol in $2005$.

d. Use the appropriate formula to determine the percentage of seniors who used alcohol in $2005$. How does this compare with your estimate in part (c )?

e. For the period from $1980$ through $2009$, in which year was marijuana use by seniors at a minimum? Estimate the percentage of seniors who used marijuana in that year.

The domain of each piecewise function is $(-\infty, \infty)$.

a. Graph each function.

b. Use your graph to determine the function's range.

$$f(x)=\left\{\begin{array}{clc}0 & \text { if } & x<-3 \\ -x & \text { if } & -3 \leq x<0 \\ x^2-1 & \text { if } & x \geq 0\end{array}\right.$$

Write each English sentence as an equation in two variables. Then graph the equation. The y-value is three decreased by the square of the x-value.

Begin by graphing the standard quadratic function, $f(x) = x^2$. Then use transformations of this graph to graph the given function.

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

Graph the given square root functions, $f$ and $g$, in the same rectangular coordinate system. Use the integer values of $x$ given to the right of each function to obtain ordered pairs. Because only nonnegative numbers have square roots that are real numbers, be sure that each graph appears only for values of $x$ that cause the expression under the radical sign to be greater than or equal to zero. Once you have obtained your graphs, describe how the graph of $g$ is related to the graph of $f$.

$f(x)=\sqrt{x} \quad(x=0,1,4,9)$ and

$$g(x)=\sqrt{x+2} \quad(x=-2,-1,2,7)$$

Graph each equation.

$y=-\frac{1}{x} \quad$ (Let $x=-2,-1, -\frac{1}{2},-\frac{1}{3}, \frac{1}{3}, \frac{1}{2}, 1$ and $2$.)

In this exercise, $f$ and $g$ are defined by the following tables. Use the tables to evaluate each composite function.

$$f(g(4))$$

The data can be described by the following mathematical models:

$$A=-0.9n +69$$

$$M= -0.3n +27.$$

a. Use the appropriate line graph to determine the percentage of seniors who used alcohol in $2000$.

b. Use the appropriate formula to determine the percentage of seniors who used alcohol in $2000$. Does the formula underestimate or overestimate the actual percentage displayed by the graph? By how much?

c. Use the appropriate line graph to estimate the percentage of seniors who used marijuana in $2000$.

d. Use the appropriate formula to determine the percentage of seniors who used marijuana in $2000$. How does this compare with your estimate in part (c )?

e. For the period from $1980$ through $2009$, in which year was alcohol use by seniors at a maximum? Estimate the percentage of seniors who used alcohol in that year.

Give the slope and $y$-intercept of each line whose equation is given. Then graph the line.

$$y=\frac{2}{5} x-1$$

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation.

$$x^2+y^2+8x+4y+16=0$$

Graph each equation in a rectangular coordinate system.

$$x=0$$

Find

a. $(f \circ g)(x) \quad$ b. $(g \circ f)(x) \quad$ c. $(f \circ g)(2) \quad$ d. $(g \circ f)(2)$.

$$f(x)=5x+2, g(x)=3x-4$$

In the said exercises, describe what important information the growers could learn from the total-yield function.

The domain of each piecewise function is $(-\infty, \infty)$.

a. Graph each function.

b. Use your graph to determine the function's range.

$$f(x)=\left\{\begin{array}{ccc}0 & \text { if } & x<-4 \\ -x & \text { if } & -4 \leq x<0 \\ x^2 & \text { if } & x \geq 0\end{array}\right.$$