91Ó°ÊÓ

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

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. $$f(x)=\frac{2 x^{2}+5 x-3}{3 x+2}$$

Use the six-step procedure to graph the rational function. Be sure to draw any asymptotes as dashed lines. $$f(x)=\frac{-x^{3}+4 x}{x^{2}-9}$$

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. $$f(x)=\frac{-x^{3}+4 x}{x^{2}-9}$$

Solve the rational inequality. Express your answer using interval notation. $$\frac{3 x-1}{x^{2}+1} \leq 1$$

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. $$f(x)=\frac{-5 x^{4}-3 x^{3}+x^{2}-10}{x^{3}-3 x^{2}+3 x-1}$$

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

Solve the rational inequality. Express your answer using interval notation. $$\frac{2 x+17}{x+1}>x+5$$

Graph the rational function by applying transformations to the graph of \(y=\frac{1}{x}\). $$f(x)=\frac{1}{x-2}$$

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. $$f(x)=\frac{18-2 x^{2}}{x^{2}-9}$$