# Sample quiz on the reciprocal of a linear function Main home here.

1. What is the equation of the horizontal asymptote of the rational function $\frac{1}{x-5}$ ?
$x=0$
$y=0$
$y=5$
$x=5$
2. What is the equation of the vertical asymptote of the rational function $\frac{1}{2x+1}$?
$x=-\frac{1}{2}$
$x=-1$
$x=\frac{1}{2}$
$y=0$
3. Relative to the parent $\frac{1}{x}$, what transformation leads to $\frac{1}{x+4}$?
a horizontal translation of $4$ units to the right
a horizontal translation of $4$ units to the left
a vertical translation of $4$ units down
a vertical translation of $4$ units up
4. What is the domain of the rational function $\frac{1}{2x-6}$?
$\{x\in\mathbf{R}| x\neq 6\}$
$\{x\in\mathbf{R}| x\neq 3\}$
$\{x\in\mathbf{R}| x\neq 2\}$
$\{x\in\mathbf{R}| x\neq 0\}$
5. Are there rational functions without vertical asymptotes?
No
Yes
Not sure
Only the reciprocal of linear functions have vertical asymptotes
6. What is the range of the rational function $\frac{-1}{3x+6}$?
$\{y\in\mathbf{R}| y\neq 0\}$
$\{y\in\mathbf{R}| y\neq 6\}$
$\{y\in\mathbf{R}| y\neq -2\}$
$\{y\in\mathbf{R}| y\neq -6\}$
7. What is the $x$-intercept of the function $\frac{2}{x-1}$
$x=0$
$x=1$
$x=-2$
The function doesn't have $x$-intercept.
8. What is the $y$-intercept of the function $\frac{1}{4-x}$
$y=4$
$y=\frac{1}{4}$
$y=0$
$y=-\frac{1}{4}$
9. If the rational function $y=\frac{k}{x-2}$ passes through the point $(1,5)$, the value of $k$ will be $\cdots\cdots$
$k=\frac{1}{5}$
$k=5$
$k=-5$
$k=-\frac{1}{5}$
10. If the parent function $\frac{1}{x}$ is reflected in the $x$-axis and then undergoes a horizontal translation of $3$ units to the left, what is the resulting equation?
$\frac{x-3}{x}$
$\frac{x}{x-3}$
$\frac{-1}{x+3}$
$\frac{-1}{x-3}$