91Ó°ÊÓ

Use a calculator to find each root or power. Give as many digits as your display shows. $$\sqrt[3]{-4}$$

Sketch a graph of each rational function. Your graph should include all asymptotes. Do not use a calculator. $$f(x)=\frac{x+2}{x-3}$$

Sketch a graph of each rational function. Your graph should include all asymptotes. Do not use a calculator. $$f(x)=\frac{x-3}{x+4}$$

Explain how the graph of \(f\) can be obtained from the graph of \(y=\frac{1}{x}\) or \(y=\frac{1}{x^{2}}\) Draw a sketch of the graph of \(f\) by hand. Then generate an accurate depiction of the graph with a graphing calculator. Finally, give the domain and range. $$f(x)=\frac{-1}{(x-4)^{2}}+2$$

Use a calculator to find each root or power. Give as many digits as your display shows. $$\sqrt[5]{-3}$$

Solve each equation by hand. Do not use a calculator. $$x^{3 / 4}-2 x^{1 / 2}-4 x^{1 / 4}+8=0$$

Use an analytic method to solve each equation in part (a). Support the solution with a graph. Then use the graph to solve the inequalities in parts (b) and (c). (a) \(\sqrt{3 x+7}=2\) (b) \(\sqrt{3 x+7}>2\) (c) \(\sqrt{3 x+7}<2\)

Sketch a graph of each rational function. Your graph should include all asymptotes. Do not use a calculator. $$f(x)=\frac{4-2 x}{8-x}$$

Use a calculator to find each root or power. Give as many digits as your display shows. $$\sqrt[3]{-125}$$

Use the methods of Examples 1 and 3 to solve the rational equation and associated inequalities given.Then, support your answer by using the \(x\) -intercept method with a calculator graph in the suggested window. (a) \(\frac{x-6}{x+2}=-1\) (b) \(\frac{x-6}{x+2}<-1\) (c) \(\frac{x-6}{x+2}>-1\) Window: \([-10,10]\) by \([-10,10]\)