91Ó°ÊÓ

Suppose that the graph of a rational function \(f\) has vertical asymptote \(x=1\) horizontal asymptote \(y=2,\) domain ( \(-\infty, 1\) ) U ( \(1, \infty\) ), and range ( \(-\infty, 2\) ) U ( \(2, \infty\) ). Give the vertical asymptote, horizontal asymptote, domain, and range for the graph of each shifted function. $$y=f(x+2)-1$$

Use a calculator to find each root or power. Give as many digits as your display shows. $$\sqrt[6]{\pi^{2}}$$

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) \(\sqrt{5 x+1}+2=2 x\) (b) \(\sqrt{5 x+1}+2>2 x\) (c) \(\sqrt{5 x+1}+2<2 x\)

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

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) \(\sqrt{3 x+4}+x=8\) (b) \(\sqrt{3 x+4}+x>8\) (c) \(\sqrt{3 x+4}+x<8\)

Use a calculator to find each root or power. Give as many digits as your display shows. $$\sqrt[6]{\pi^{-1}}$$

Sketch a graph of each rational function. Your graph should include all asymptotes. Do not use a calculator. $$f(x)=\frac{(x+6)(x-2)}{(x+3)(x-4)}$$

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) \(\sqrt{3 x-6}+2=\sqrt{5 x-6}\) (b) \(\sqrt{3 x-6}+2>\sqrt{5 x-6}\) (c) \(\sqrt{3 x-6}+2<\sqrt{5 x-6}\)

Use a calculator to find each root or power. Give as many digits as your display shows. $$13^{-1 / 3}$$

Sketch a graph of each rational function. Your graph should include all asymptotes. Do not use a calculator. $$f(x)=\frac{(x+3)(x-5)}{(x+1)(x-4)}$$