91Ó°ÊÓ

What is an exponential function?

Describe the shape of a scatter plot that suggests modeling the data with an exponential function.

The graphs of solution sets of systems of inequalities involve finding the intersection of the solution sets of two or more inequalities. By contrast, in Exercises 43-44, you will be graphing the union of the solution sets of two inequalities. Graph the union of \(x-y \geq-1\) and \(5 x-2 y \leq 10\).

Describe the shape of a scatter plot that suggests modeling the data with a quadratic function.

Many elevators have a capacity of 2000 pounds. a. If a child averages 50 pounds and an adult 150 pounds, write an inequality that describes when \(x\) children and \(y\) adults will cause the elevator to be overloaded. b. Graph the inequality. Because \(x\) and \(y\) must be positive, limit the graph to quadrant I only. c. Select an ordered pair satisfying the inequality. What are its coordinates and what do they represent in this situation?

Evaluate \(f(x)\) for the given values of \(x\). Then use the ordered pairs \((x, f(x))\) from your table to graph the function. $$ \begin{aligned} &f(x)=x-1\\\ &\begin{array}{|r|l|} \hline {}{}{\boldsymbol{c}} & \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}-1 \\\ \hline-2 & \\ \hline-1 & \\ \hline 0 & \\ \hline 1 & \\ \hline 2 & \\ \hline \end{array} \end{aligned} $$

Evaluate \(f(x)\) for the given values of \(x\). Then use the ordered pairs \((x, f(x))\) from your table to graph the function. $$ \begin{aligned} &f(x)=x^{3}+1\\\ &\begin{array}{|r|c|} \hline {}{}{x} & f(x)=x^{3}+1 \\ \hline-3 & \\ \hline-2 & \\ \hline-1 & \\ \hline 0 & \\ \hline 1 & \\ \hline \end{array} \end{aligned} $$

What is a half-plane?

What does a dashed line mean in the graph of an inequality?

Compare the graphs of \(3 x-2 y>6\) and \(3 x-2 y \leq 6\). Discuss similarities and differences between the graphs.