91Ó°ÊÓ

Use a calculator to find each root or power. Give as many digits as your display shows. $$(2 \pi)^{4 / 3}$$

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). 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) \((x+5)^{1 / 2}-2=(x-1)^{1 / 2}\) (b) \((x+5)^{1 / 2}-2 \geq(x-1)^{1 / 2}\) (c) \((x+5)^{1 / 2}-2 \leq(x-1)^{1 / 2}\)

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

Solve each equation and inequality. (a) \(\frac{\left(x^{2}-1\right)(3)-(3 x-1)(2 x)}{\left(x^{2}-1\right)^{2}}=0\) (b) \(\frac{\left(x^{2}-1\right)(3)-(3 x-1)(2 x)}{\left(x^{2}-1\right)^{2}} \leq 0\)

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) \(\left(x^{2}+6 x\right)^{1 / 4}=2\) (b) \(\left(x^{2}+6 x\right)^{1 / 4}>2\) (c) \(\left(x^{2}+6 x\right)^{1 / 4}<2\)

Sketch a graph of each rational function. Your graph should include all asymptotes. Do not use a calculator. $$f(x)=\frac{x}{x^{2}-9}$$

Evaluate \(f(x)\) at the given \(x\). Approximate each result to the nearest hundredth. $$f(x)=x^{1.62}, \quad x=1.2$$

Solve each equation and inequality. (a) \(\frac{(2 x+1)(2 x)-\left(x^{2}+1\right)(2)}{(2 x+1)^{2}}=0\) (b) \(\frac{(2 x+1)(2 x)-\left(x^{2}+1\right)(2)}{(2 x+1)^{2}}<0\)

Sketch a graph of each rational function. Your graph should include all asymptotes. Do not use a calculator. $$f(x)=\frac{-5}{2 x+4}$$

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) \(\left(x^{2}+2 x\right)^{1 / 4}=3^{1 / 4}\) (b) \(\left(x^{2}+2 x\right)^{1 / 4}>3^{1 / 4}\) (c) \(\left(x^{2}+2 x\right)^{1 / 4}<3^{1 / 4}\)