Sample quiz on reciprocal of quadratic functions
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  1. What is the horizontal asymptote of the rational function $\frac{1}{(x-1)(x+1)}$?
    $y=0$
    $y=1$
    $y=-1$
    $y=-2$
  2. What is(are) the vertical asymptote(s) of the rational function $\frac{1}{x^2-4}$?
    $x=2$
    $x=-2$
    $x=-2,2$
    $x=-4,4$
  3. What is the domain of the rational function $\frac{1}{x^2+9}$?
    $\{x\in\mathbf{R}|x\neq 3\}$
    $\{x\in\mathbf{R}|x\neq \pm 3\}$
    $\{x\in\mathbf{R}|x\neq \pm 9\}$
    $\{x\in\mathbf{R}\}$
  4. What is the $y$-intercept of the rational function $\frac{1}{(2x-3)(x+1)}$?
    $y=-3$
    $y=-\frac{1}{3}$
    $y=-\frac{3}{2}$
    $y=\frac{1}{3}$
  5. As $x\rightarrow -4^{+}$, the rational function $\frac{1}{x^2-16}$ approaches what value?
    $0$
    $4$
    $\infty$
    $-\infty$
  6. If $x=-2$ is one of the vertical asymptotes of the rational function $\frac{1}{x^2+bx-8}$, what is the value of $b$?
    $b=4$
    $b=-2$
    $b=-4$
    $b=-6$
  7. Find the range of $\frac{-1}{x^2+1}$.
    $\{y\in\mathbf{R}|y\neq 1\}$
    $\{y\in\mathbf{R}|y\neq 0\}$
    $\{y\in\mathbf{R}|y\neq -1\}$
    $\{y\in\mathbf{R}\}$
  8. Find the value of $k$ for which $\frac{k}{(x+2)(x-1)}$ contains the point $(-1,-1)$.
    $k=2$
    $k=\frac{1}{2}$
    $k=-\frac{1}{2}$
    $k=-2$
  9. Within what interval is the function $\frac{1}{x^2-8x+16}$ negative?
    Values of $x$ greater than $4$
    Values of $x$ less than $4$
    Values of $x$ between $-4$ and $4$
    The function is always positive
  10. What is the equation of the reciprocal of a quadratic function with vertical asymptotes at $x=-2$ and $x=3$?
    $y=\frac{1}{x^2-x+6}$
    $y=\frac{1}{x^2+x-6}$
    $y=\frac{1}{x^2-x-6}$
    $y=\frac{-1}{x^2-x+6}$