91Ó°ÊÓ

Why does the vertical line test tell us whether the graph of a relation represents a function?

For the following exercises, find the domain of each function using interval notation. $$f(x)=\sqrt{x^{2}+4}$$

For the following exercises, sketch a graph of the piecewise function. Write the domain in interval notation. $$f(x)=\left\\{\begin{array}{ll}{3} & {\text { if } x < 0} \\ {\sqrt{x}} & {\text { if } x \geq 0}\end{array}\right.$$

At the start of a trip, the odometer on a car read 21,395. At the end of the trip, 13.5 hours later, the odometer read 22,125. Assume the scale on the odometer is in miles. What is the average speed the car traveled during this trip?

For the following exercises, use the function values for \(f\) and \(g\) shown in Table 1.24 to evaluate the expressions. $$ \begin{array}{|c|c|c|c|c|c|c|c|}\hline x & {-3} & {-2} & {-1} & {0} & {1} & {2} & {3} \\ \hline f(x) & {11} & {9} & {7} & {5} & {3} & {1} & {-1} \\\ \hline g(x) & {-8} & {-3} & {0} & {1} & {0} & {-3} & {-8} \\\ \hline\end{array} $$ $$ (g \circ g)(1) $$

A forest fire leaves belind an area of grass burned in an expanding circular pattern. If the radius of the circle of burning grass is increasing with time according to the formula \(r(t)=2 t+1,\) express the area burned as a function of time, \(t\) (minutes).

When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal shiff from a vertical shift?

For the following exercises, solve the equations below and express the answer using set notation. $$|6-x|=5$$

For the following exercises, find the \(x\) - and \(y\) -intercepts of the graphs of each function. $$f(x)=2|x+1|-10$$

For the following exercises, solve each inequality and write the solution in interval notation. $$|3 x-5| \geq-13$$