91Ó°ÊÓ

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

Use the six-step procedure to graph the rational function. Be sure to draw any asymptotes as dashed lines. $$f(x)=\frac{1}{x^{2}+x-12}$$

Solve the rational equation. Be sure to check for extraneous solutions. $$\frac{x^{2}-2 x+1}{x^{3}+x^{2}-2 x}=1$$

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. $$f(x)=\frac{x^{2}-x-12}{x^{2}+x-6}$$

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

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

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

Graph the rational function by applying transformations to the graph of \(y=\frac{1}{x}\). $$g(x)=1-\frac{3}{x}$$

Graph the rational function by applying transformations to the graph of \(y=\frac{1}{x}\). $$j(x)=\frac{3 x-7}{x-2}$$

A right cylindrical drum is to hold 7.35 cubic feet of liquid. Find the dimensions (radius of the base and height) of the drum which would minimize the surface area. What is the minimum surface area? Round your answers to two decimal places.