91Ó°ÊÓ

Solve the rational inequality. Express your answer using interval notation. $$\frac{x}{x^{2}-1}>0$$

Use the six-step procedure to graph the rational function. Be sure to draw any asymptotes as dashed lines. $$f(x)=\frac{x^{2}-x-12}{x^{2}+x-6}$$

Use the six-step procedure to graph the rational function. Be sure to draw any asymptotes as dashed lines. $$f(x)=\frac{3 x^{2}-5 x-2}{x^{2}-9}$$

For the given rational function \(f\) : \(\bullet\)Find the domain of \(f\). \(\bullet\)Identify any vertical asymptotes of the graph of \(y=f(x)\) \(\bullet\)Identify any holes in the graph. \(\bullet\)Find the horizontal asymptote, if it exists. \(\bullet\)Find the slant asymptote, if it exists. \(\bullet\)Graph the function using a graphing utility and describe the behavior near the asymptotes. $$f(x)=\frac{3 x^{2}-5 x-2}{x^{2}-9}$$

Solve the rational inequality. Express your answer using interval notation. $$\frac{4 x}{x^{2}+4} \geq 0$$

For the given rational function \(f\) : \(\bullet\)Find the domain of \(f\). \(\bullet\)Identify any vertical asymptotes of the graph of \(y=f(x)\) \(\bullet\)Identify any holes in the graph. \(\bullet\)Find the horizontal asymptote, if it exists. \(\bullet\)Find the slant asymptote, if it exists. \(\bullet\)Graph the function using a graphing utility and describe the behavior near the asymptotes. $$f(x)=\frac{x^{3}+2 x^{2}+x}{x^{2}-x-2}$$

Solve the rational inequality. Express your answer using interval notation. $$\frac{x^{2}-x-12}{x^{2}+x-6}>0$$

Use the six-step procedure to graph the rational function. Be sure to draw any asymptotes as dashed lines. $$f(x)=\frac{x^{2}-x-6}{x+1}$$

For the given rational function \(f\) : \(\bullet\)Find the domain of \(f\). \(\bullet\)Identify any vertical asymptotes of the graph of \(y=f(x)\) \(\bullet\)Identify any holes in the graph. \(\bullet\)Find the horizontal asymptote, if it exists. \(\bullet\)Find the slant asymptote, if it exists. \(\bullet\)Graph the function using a graphing utility and describe the behavior near the asymptotes. $$f(x)=\frac{x^{3}-3 x+1}{x^{2}+1}$$

Solve the rational inequality. Express your answer using interval notation. $$\frac{3 x^{2}-5 x-2}{x^{2}-9}<0$$