91Ó°ÊÓ

In Exercises \(31-40,\) write the standard form of the equation of the circle with the given center and radius. $$\text { Center }(0,0), r=7$$

The figure shows an open box with a square base. The box is to have a volume of 10 cubic feet. Express the amount of material needed to construct the box, \(A\), as a function of the length of a side of its square base, \(x\).

Find \(f+g, f-g,\) fg, and \(\frac{f}{8} .\) Determine the domain for each function. $$f(x)=3 x-4, g(x)=x+2$$

The figure shows a package whose front is a square. The length plus girth (the distance around) of the package is 300 inches. (This is the maximum length plus girth permitted by Federal Express for its overnight service.) Express the volume of the package, \(V,\) as a function of the length of a side of its square front, \(x\).

What is a secant line?

Let \(P(x, y)\) be a point on the graph of \(y=\sqrt{x} .\) Express the distance, \(d,\) from \(P\) to \((1,0)\) as a function of the point's \(x\) -coordinate.

In Exercises \(39-50,\) graph the given functions, \(f\) and \(g,\) in the same rectangular coordinate system. Select integers for \(x\), starting with \(-2\) and ending with \(2 .\) Once you have obtained your graphs, describe how the graph of g is related to the graph of \(f\). $$f(x)=x, g(x)=x+3$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I have linear functions that model changes for men and women over the same time period. The functions have the same slope, so their graphs are parallel lines, indicating that the rate of change for men is the same as the rate of change for women.

Two vertical poles of length 6 feet and 8 feet, respectively, stand 10 feet apart. A cable reaches from the top of one pole to some point on the ground between the poles and then to the top of the other pole. Express the amount of cable used, \(f,\) as a function of the distance from the 6 -foot pole to the point where the cable touches the ground, \(x\).

a. Find an equation for \(f^{-1}(x)\). b. Graph \(f\) and \(f^{-1}\) in the same rectangular coordinate system. c. Use interval notation to give the domain and the range of \(f\) and \(f^{-1}\). $$f(x)=(x+2)^{3}$$