5. Rational Functions

Sketch the graph of the function $f\left(x\right)=\frac{1}{x^2}$. Identify the asymptotes on the graph.

Based only on the vertical asymptotes, which of the following graphs could be the graph of the given function? $f\left(x\right)=\frac{x^2-4x}{x^2-x-12}$

Find all vertical asymptotes and holes of each function.

$f\left(x\right)=\frac{-5x}{\left(2x-3\right)^2}$

Find all vertical asymptotes and holes of each function.

$f\left(x\right)=\frac{x^2-2x}{2x^3-x^2-6x}$

Find all vertical asymptotes and holes of each function.

$f\left(x\right)=\frac{x^2+10x+25}{2x^2+8x-10}$

Find the horizontal asymptote of each function.

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

Find the horizontal asymptote of each function.

$f\left(x\right)=\frac{8x^2+1}{2x^2-x-6}$

Find the horizontal asymptote of each function.

$f\left(x\right)=\frac{x^2+4x}{2x^3+8x^2}$

Find the domain of each rational function. g(x)=3x²/(x−5)(x+4)

Find the domain of each rational function. h(x)=(x+7)/(x²−49)

Use the graphs of the rational functions in choices A–D to answer each question.

There may be more than one correct choice. Which choices have domain (-∞, 3)U(3, ∞)?

Use the graph of the rational function in the figure shown to complete each statement in Exercises 9–14.

As $x\to 1^{-},f\left(x\right){\to }_{{}_{}}$______

Use the graph of the rational function in the figure shown to complete each statement in Exercises 9–14.

As $x\to -\infty ,f\left(x\right){\to }_{{}_{}}$_____

Use the graph of the rational function in the figure shown to complete each statement in Exercises 15–20.

As $x\to 1^{+},f\left(x\right)\to$ __

Match the rational function in Column I with the appropriate description in Column II. Choices in Column II can be used only once.

$\text{ƒ}\left(x\right)=\frac{(x+7)}{(x+1)}$