Sample quiz on rational functions of the form $\frac{ax+b}{cx+d}$
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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 $\frac{x}{1-x}$?
    
    $\{y\in\mathbb{R}~|~y\neq 0\}$
    $\{y\in\mathbb{R}~|~y\neq 1\}$
    $\{y\in\mathbb{R}~|~y\neq -1\}$
    $\{y\in\mathbb{R}~|~y\neq -2\}$