91Ó°ÊÓ

Sales The monthly sales \(S\) (in thousands of units) of a seasonal product are modeled by $$S=58.3+32.5 \cos \frac{\pi t}{6}$$ where \(t\) is the time (in months), with \(t=1\) corresponding to January. Use a graphing utility to graph the model for \(S\) and determine the months when sales exceed \(75,000\) units.

Even and Odd Functions and zeros of Functions In Exercises \(75-78\) , determine whether the function is even, odd, or neither. Then find the zeros of the function. Use a graphing utility to verify your result. $$f(x)=\sqrt[3]{x}$$

Distance Write the distance \(d\) between the point \((3,1)\) and the line \(y=m x+4\) in terms of \(m .\) Use a graphing utility to graph the equation. When is the distance 0\(?\) Explain the result geometrically.

Writing Functions In Exercises 79-82, write an equation for a function that has the given graph. $$$$Line segment connecting \((-2,4)\) and \((0,-6)\)

Sketching a Graph In Exercises \(83-86,\) sketch a possible graph of the situation. $$\begin{array}{l}{\text { The height of a baseball as a function of horizontal distance }} \\ {\text { during a home run }}\end{array}$$

Proof Prove that if the slopes of two nonvertical lines are negative reciprocals of each other, then the lines are perpendicular.

Domain Find the value of \(c\) such that the domain of $$\begin{array}{l}{f(x)=\sqrt{c-x^{2}}} \\ {\text { is }[-5,5]}\end{array}$$

Polynomial Functions Does the degree of a polynomial function determine whether the function is even or odd? Explain.

A vertical line can intersect the graph of a function at most once.

If the domain of a function consists of a single number, then its range must also consist of only one number.