Does the table represent a linear or nonlinear function? Explain.

$$\begin{matrix} \text{x} & \text{-5} & \text{-1} & \text{3} & \text{7}\\ \text{y} & \text{14} & \text{12} & \text{10} & \text{8}\\ \end{matrix}$$

A certain coffeehouse chain has been adding stores across the country for many years. The number of locations is given by N(t), where t is measured in years. Selected values for N(t) are given in the tuble.

(a) Find the average rate of growth

(i) from 2008 to 2010.

(ii) from 2010 to 2012

Indicate the units of measure. What do your answers suggest about the growth of locatsons?

(b) Estimate the instantaneous growth in 2015. Indicale the units of measure.

Growth of a Human Population The population of a town is growing exponentially.

Graph the function using a graphing utility.

Solve each system.

$$\left\{\begin{array}{l}{y=-x^{2}-x-3} \\ {y=2 x^{2}-2 x-3}\end{array}\right.$$

Graph each inequality or system of inequalities.

$$\left. \begin{array} { l } { | x | \leq 2 } \\ { | y | \leq 3 } \end{array} \right.$$

Graph the solutions to the system of inequalities at right.

$$\begin{array} { l } { y \geq \frac { 2 } { 3 } x - 7 } \\ { y < - x + 4 } \end{array}$$

Rotate the figure the given number of degrees 180$^\circ$ about the origin. List the coordinates of the vertices of the image.

The vertices of the image are at A(-2,0), B(-3,2), C(-2,4), and D(-1,2).

Growth of an Insect Population An insect population grows exponentially. When will the population reach 700 ?

Briefly discuss the link between desertification and population growth.

Classify the statement as either true or false.

$3 t+1=7$ and $8-2=9$ are both equations.

Solve each system of inequalities by graphing.

$$\left. \begin{array} { l } { x > - 3 } \\ { - 3 x + y \geq 6 } \end{array} \right.$$

Sketch the graph of a nonlinear function with y-intercept -4, increasing function values for x < 2 and 0 < x < 2, decreasing function values for -2 < x < 0 and x > 2, and the following end behavior, as $x \rightarrow \infty, f(x) \rightarrow-\infty \text { and as } x \rightarrow-\infty$, $f(x) \rightarrow-x$.

Considering the survival rate for new magazines, why do media companies view crossovers to be a smart way to create new revenues?

(a) What does "the toe of his father's heavy shoe," mentioned in the last line of the story, symbolize?

(b) In what way does this symbol capture John's relationship to Gabriel?

(c) How would you define their relationship at the end of the story?