91Ó°ÊÓ

Find a function of the form \(f(x)=a e^{b x}\) with the given function values. $$f(0)=5, f(1)=2$$

A brief description is given of a physical situation. For the indicated variable, state a reasonable domain. A new candy bar is to be sold; \(x=\operatorname{cost}\) of candy bar (in cents).

State a rule for transforming the eraph of \(y=f(x)\) into the graph of \(y=f(c x)\) for \(c<0\)

Use the range for \(\theta\) to determine the indicated function value. $$\cos \theta=\frac{4}{5}, 0 \leq \theta \leq \frac{\pi}{2} ; \quad \text { find } \sin \theta$$

Determine the number of (real) solutions. Solve for the intersection points exactly if possible and estimate the points if necessary. $$(x+1)^{2 / 3}=2-x$$

A fast-food restaurant gives every customer a game ticket. With each ticket, the customer has a 1 -in- 10 chance of winning a free meal. If you go 10 times, estimate your chances of winning at least one free meal. The exact probability is \(1-\left(\frac{9}{10}\right)^{10} .\) Compute this number and compare it to your guess.

Discuss whether you think \(y\) would be a function of \(x\). \(y=\) grade you get on an exam, \(x=\) number of hours you study.

Use the range for \(\theta\) to determine the indicated function value. $$\sin \theta=\frac{1}{2}, \frac{\pi}{2} \leq \theta \leq \pi ; \quad \text { find } \cos \theta$$

Determine the number of (real) solutions. Solve for the intersection points exactly if possible and estimate the points if necessary. $$\cos x=x^{2}-1$$

Explain why the graph of \(y=|x|^{3}\) is identical to that of \(y=x^{3}\) to the right of the y-axis. For \(y=|x|^{3}\), describe how the graph to the left of the \(y\) -axis compares to the graph to the right of the \(y\) -axis. In general, describe how to draw the graph of \(y=f(|x|)\) given the graph of \(y=f(x)\)