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Magazine Problem 1
Use the six-step procedure to graph the rational function. Be sure to draw any asymptotes as dashed lines. $$f(x)=\frac{4}{x+2}$$
Problem 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. $$f(x)=\frac{x}{3 x-6}$$
Problem 1
Solve the rational equation. Be sure to check for extraneous solutions. $$\frac{x}{5 x+4}=3$$
Problem 2
Solve the rational equation. Be sure to check for extraneous solutions. $$\frac{3 x-1}{x^{2}+1}=1$$
Problem 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. $$f(x)=\frac{3+7 x}{5-2 x}$$
Problem 3
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. $$f(x)=\frac{x}{x^{2}+x-12}$$
Problem 3
Solve the rational equation. Be sure to check for extraneous solutions. $$\frac{1}{x+3}+\frac{1}{x-3}=\frac{x^{2}-3}{x^{2}-9}$$
Problem 4
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. $$f(x)=\frac{x}{x^{2}+1}$$
Problem 4
Use the six-step procedure to graph the rational function. Be sure to draw any asymptotes as dashed lines. $$f(x)=\frac{1}{x^{2}+x-12}$$
Problem 4
Solve the rational equation. Be sure to check for extraneous solutions. $$\frac{2 x+17}{x+1}=x+5$$
