# Sample quiz on rational functions of the form $\frac{ax+b}{cx+d}$ Main home here.

1. What is the equation of the horizontal asymptote of the rational function $y=\frac{3x}{x-3}$?
$y=\frac{1}{3}$
$y=3$
$y=0$
$x=3$
2. What is the equation of the vertical asymptote of the rational function $y=\frac{x}{2x-4}$?
$x=0$
$x=2$
$x=4$
$y=1$
3. What is the $x$-intercept of the function $y=\frac{x-2}{x+2}$?
$x=-2$
$x=-1$
$x=1$
$x=2$
4. What is the $y$-intercept of the rational function $y=\frac{2x-3}{3x+2}$?
$-\frac{3}{2}$
$-\frac{2}{3}$
$\frac{3}{2}$
$\frac{2}{3}$
5. Which of the rational functions below has a vertical asymptote at $x=-4$ and a $y$-intercept of $\frac{1}{2}$?
$\frac{2}{(x-4)^2}$
$\frac{2}{(x+4)^2}$
$\frac{2}{x+4}$
$\frac{2}{x-4}$
6. Find the equation of a rational function with a vertical asymptote $x=6$ and passes through $(5,6)$
$y=\frac{6}{x-6}$
$y=\frac{6}{x+6}$
$y=\frac{-6}{x+6}$
$y=\frac{-6}{x-6}$
7. A rational function has $y=2$ and $x=3$ as its horizontal and vertical asymptotes, respectively. Which of the equations below fits it?
$y=\frac{2x+6}{x-3}$
$y=\frac{3x-6}{x-3}$
$y=\frac{2x-6}{x+3}$
$y=\frac{3x+6}{x-2}$
8. What is the domain of the rational function $y=\frac{2x-8}{x+4}$
$\{x\in\mathbb{R}~|~x\neq 4\}$
$\{x\in\mathbb{R}~|~x\neq 8\}$
$\{x\in\mathbb{R}~|~x\neq -4\}$
$\{x\in\mathbb{R}~|~x\neq -8\}$
9. What is the range of the rational function $\frac{x+1}{3x-2}$
$\{y\in\mathbb{R}~|~y\neq 2\}$
$\{y\in\mathbb{R}~|~y\neq 3\}$
$\{y\in\mathbb{R}~|~y\neq \frac{2}{3}\}$
$\{y\in\mathbb{R}~|~y\neq \frac{1}{3}\}$
10. What is the range of the rational function $\frac{x}{1-x}$?
$\{y\in\mathbb{R}~|~y\neq 0\}$
$\{y\in\mathbb{R}~|~y\neq 1\}$
$\{y\in\mathbb{R}~|~y\neq -1\}$
$\{y\in\mathbb{R}~|~y\neq -2\}$