5. Rational Functions

Work each problem. Choices A–D below show the four ways in which the graph of a rational function can approach the vertical line x=2 as an asymptote. Identify the graph of each rational function defined in parts (a) – (d). $\text{ƒ}\left(x\right)=1/(x-2)$

Graph each rational function. ƒ(x)=(6-3x)/(4-x)

Graph each rational function. ƒ(x)=5x/(x²-1)

Graph each rational function. See Examples 5–9.

$\text{ƒ}\left(x\right)=\left[\right(x+6\left)\right(x-2\left)\right]/\left[\right(x+3\left)\right(x-4\left)\right]$

Graph each rational function. ƒ(x)=[(x+3)(x-5)]/[(x+1)(x-4)]

Graph each rational function. ƒ(x)=(x²+8x+16)/(x²+4x-5)

Graph each rational function. ƒ(x)=(x²+2x+1)/(x²-x-6)

Graph each rational function. ƒ(x)=(20+6x-2x²)/(8+6x-2x²)

Graph each rational function. ƒ(x)=(18+6x-4x²)/(4+6x+2x²)

Provide a short answer to each question. What is the domain of the function $\text{ƒ}\left(x\right)=\frac{1}{x^2}$? What is its range?

Graph each rational function. ƒ(x)=(9x²-1)/(x²-4)

Graph each rational function. See Examples 5–9.

$\text{ƒ}\left(x\right)=(16x^2-9)/(x^2-9)$

Provide a short answer to each question. What is the equation of the vertical asymptote of the graph of y=[1/(x-3)]+2? Of the horizontal asymptote?

Work each problem. Which function has a graph that does not have a vertical asymptote?

A. ƒ(x)=1/(x²+2)

B. ƒ(x)=1/(x²-2)

C. ƒ(x)=3/x²

D. ƒ(x)=(2x+1)/(x-8)

Identify any vertical, horizontal, or oblique asymptotes in the graph of y=ƒ(x). State the domain of ƒ.