Chapter 5

Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. State the domain of \(f .\) $$f(x)=\frac{x^{2}-2 x-3}{2 x^{2}-x-10}$$

Solve each equation by hand. Do not use a calculator. $$\sqrt[3]{x+1}=-3$$

Evaluate each expression. $$-81^{0.5}$$

Find all complex solutions for each equation by hand. $$\frac{2}{x^{2}-2 x}-\frac{3}{x^{2}-x}=0$$

Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. State the domain of \(f .\) $$f(x)=\frac{3 x^{2}-6 x-24}{5 x^{2}-26 x+5}$$

Solve each equation by hand. Do not use a calculator. $$\sqrt[3]{x+9}=2$$

Evaluate each expression. $$32^{1 / 5}$$

Find all complex solutions for each equation by hand. $$1-\frac{13}{x}+\frac{36}{x^{2}}=0$$

For function find all asymptotes and the coordinates of any holes in its graph. $$f(x)=\frac{2 x^{2}+1}{3 x^{2}+4 x-4}$$

Solve each equation by hand. Do not use a calculator. $$\sqrt[3]{3 x^{2}+7}=\sqrt[3]{7-4 x}$$

Evaluate each expression. $$64^{1 / 6}$$

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. $$f(x)=\frac{2}{x}$$

Find all complex solutions for each equation by hand. $$1-\frac{3}{x}-\frac{10}{x^{2}}=0$$

For function find all asymptotes and the coordinates of any holes in its graph. $$f(x)=\frac{3 x^{2}+x-1}{2 x^{2}+3 x-2}$$

Solve each equation by hand. Do not use a calculator. $$\sqrt[3]{2 x^{2}+1}=\sqrt[3]{1-x}$$

Evaluate each expression. $$16^{-0.25}$$

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. $$f(x)=\frac{3}{x}$$

Find all complex solutions for each equation by hand. $$1+\frac{3}{x}=\frac{5}{x^{2}}$$

For function find all asymptotes and the coordinates of any holes in its graph. $$f(x)=\frac{x^{2}-2 x+3}{x+3}$$

Solve each equation by hand. Do not use a calculator. $$\sqrt[4]{x-2}+4=6$$

Evaluate each expression. $$\left(-9^{3 / 4}\right)^{2}$$

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. $$f(x)=\frac{1}{x+2}$$

Find all complex solutions for each equation by hand. $$4+\frac{7}{x}=-\frac{1}{x^{2}}$$

For function find all asymptotes and the coordinates of any holes in its graph. $$f(x)=\frac{1-2 x+x^{2}}{x-5}$$

Solve each equation by hand. Do not use a calculator. $$\sqrt[4]{2 x+3}=\sqrt{x+1}$$

Evaluate each expression. $$\left(4^{-1 / 2}\right)^{-4}$$

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. $$f(x)=\frac{1}{x-3}$$

Find all complex solutions for each equation by hand. $$\frac{x}{2-x}+\frac{2}{x}-5=0$$

For function find all asymptotes and the coordinates of any holes in its graph. $$f(x)=\frac{x+2}{x^{2}-4}$$

Solve each equation by hand. Do not use a calculator. $$x^{2 / 5}=4$$

Use positive rational exponents to rewrite each expression. Assume variables represent positive numbers. $$\sqrt[3]{2 x}$$

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. $$f(x)=\frac{1}{x}+1$$

Find all complex solutions for each equation by hand. $$\frac{2 x}{x-3}+\frac{4}{x}-6=0$$

For function find all asymptotes and the coordinates of any holes in its graph. $$f(x)=\frac{x^{2}+2 x-15}{x^{2}-2 x-3}$$

Solve each equation by hand. Do not use a calculator. $$x^{2 / 3}=16$$

Use positive rational exponents to rewrite each expression. Assume variables represent positive numbers. $$\sqrt{x+1}$$

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. $$f(x)=\frac{1}{x}-2$$

Find all complex solutions for each equation by hand. $$x^{-4}-3 x^{-2}-4=0$$

For function find all asymptotes and the coordinates of any holes in its graph. $$f(x)=\frac{x^{2}-1}{x^{2}-x-2}$$

Solve each equation by hand. Do not use a calculator. $$2 x^{1 / 3}-5=1$$

Use positive rational exponents to rewrite each expression. Assume variables represent positive numbers. $$\sqrt[3]{z^{5}}$$

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. $$f(x)=\frac{1}{x-1}+1$$

Find all complex solutions for each equation by hand. $$x^{-4}-5 x^{-2}-36=0$$

For function find all asymptotes and the coordinates of any holes in its graph. $$f(x)=\frac{8-2 x^{2}}{x^{2}-2 x}$$

Solve each equation by hand. Do not use a calculator. $$4 x^{3 / 2}+5=21$$

Use positive rational exponents to rewrite each expression. Assume variables represent positive numbers. $$\sqrt[5]{x^{2}}$$

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. $$f(x)=\frac{2}{x+2}-1$$

Find all complex solutions for each equation by hand. $$\frac{1}{x+2}+\frac{3}{x+7}=\frac{5}{x^{2}+9 x+14}$$

Write a formula for a rational function with vertical asymptotes \(x=\pm 2\) and horizontal asymptote \(y=3\)

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