91Ó°ÊÓ

Use radical notation to rewrite. $$ a^{-2 / 3} b^{3 / 5} $$

Transformations Use transformations of the graph of either \(f(x)=\frac{1}{x}\) or \(h(x)=\frac{1}{x^{2}}\) to sketch a graph of \(y=g(x)\) by hand. Show all asymptotes. Write \(g(x)\) in terms of either \(f(x)\) or \(h(x)\) $$ g(x)=\frac{1}{x-2}+1 $$

Solve the rational inequality (a) symbolically and (b) graphically. $$ \frac{1}{x}<0 $$

Solve the rational inequality. $$ \frac{3}{2-x}>\frac{x}{2+x} $$

Complete the following. (a) Find any slant or vertical asymptotes. (b) Graph \(y=f(x) .\) Show all asymptotes. $$ f(x)=\frac{4 x^{2}+x-2}{4 x-3} $$

A cardboard box with no top and a square base is being constructed and must have a volume of 108 cubic inches. Let \(x\) be the length of a side of its base in inches. (a) Write a formula \(A(x)\) that calculates the outside surface area in square feet of the box. (b) If cardboard costs \(\$ 0.10\) per square foot, write a formula \(C(x)\) that gives the cost in dollars of the cardboard in the box. (c) Find the dimensions of the box that would minimize the cost of the cardboard.

Find the constant of proportionality \(k\) $$ y=\frac{k}{x^{2}} \text { and } y=\frac{1}{4} \text { when } x=8 $$

The volume \(V\) of a cylinder with a fixed height is directly proportional to the square of its radius \(r\). If a cylinder with a radius of 10 inches has a volume of 200 cubic inches, what is the volume of a cylinder with the same height and a radius of 5 inches?

The frequency \(F\) of \(a\) vibrating string is directly proportional to the square root of the tension \(T\) on the string and inversely proportional to the length \(L\) of the string. Give two ways to double the frequency \(F\).