Sample quiz on the reciprocal of a linear function
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  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?
    $\frac{x-3}{x}$
    $\frac{x}{x-3}$
    $\frac{-1}{x+3}$
    $\frac{-1}{x-3}$