91Ó°ÊÓ

A central angle in a circle of radius 8 is subtended by an arc of length \(10 \pi .\) Find the angle's radian and degree measures.

Sketch the given curves together in the appropriate coordinate plane and label each curve with its equation. $$y=-e^{x} \text { and } y=-e^{-x}$$

One of \(\sin x, \cos x,\) and tan \(x\) is given. Find the other two if \(x\) lies in the specified interval. $$\tan x=\frac{1}{2}, \quad x \in\left[\pi, \frac{3 \pi}{2}\right]$$

Use graphs to find approximate solutions. $$3^{x}-0.5=0$$

Tell how many units and in what directions the graphs of the given equations are to be shifted. Give an equation for the shifted graph. Then sketch the original and shifted graphs together, labeling each graph with its equation. \(y=x^{3} \quad\) Left \(1,\) down 1.

Tell how many units and in what directions the graphs of the given equations are to be shifted. Give an equation for the shifted graph. Then sketch the original and shifted graphs together, labeling each graph with its equation. \(y=x^{2 / 3} \quad\) Right \(1,\) down 1

Graph \(y=\sin x\) and \(y=\lfloor\sin x\rfloor\) together. What are the domain and range of \(\lfloor\sin x\rfloor ?\)

Tell how many units and in what directions the graphs of the given equations are to be shifted. Give an equation for the shifted graph. Then sketch the original and shifted graphs together, labeling each graph with its equation. \(y=-\sqrt{x} \quad\) Right 3

Use an exponential model and a graphing calculator to estimate the answer in each problem. The population of Silver Run in the year 1890 was \(6250 .\) Assume the population increased at a rate of \(2.75 \%\) per year. a. Estimate the population in 1915 and 1940. b. Approximately when did the population reach \(50,000 ?\)

What symmetries, if any, do the graphs have? Specify the intervals over which the function is increasing and the intervals where it is decreasing. $$y=\sqrt{|x|}$$