Vertical and Horizontal Asymptotes of Rational Function Practice

1. $h(x)=\dfrac{x^2+4x-32}{x^2-8x+16}$

   At each of the following values of $x$, select whether $h$ has a zero, a vertical asymptote, or a removable discontinuity.

   • Zero
   • Vertical Asymptote

   • Removable Discontinuity

   $x=-8$

   $x=4$

2. $q(x)=\dfrac{x^2+6x+8}{x+4}$

   At each of the following values of $x$, select whether $q$ has a zero, a vertical asymptote, or a removable discontinuity.

   • Zero
   • Vertical Asymptote

   • Removable Discontinuity

   $x=-4$

   $x=-2$

3. $f(x)=\dfrac{x^2-2x-24}{x^2+10x+24}$

   At each of the following values of $x$, select whether $f$ has a zero, a vertical asymptote, or a removable discontinuity.

   • Zero
   • Vertical Asymptote

   • Removable Discontinuity

   $x=-6$

   $x=-4$

   $x=6$

4. $q(x)=\dfrac{x+8}{x^2-10x+9}$

   At each of the following values of $x$, select whether $q$ has a zero, a vertical asymptote, or a removable discontinuity.

   • Zero
   • Vertical Asymptote

   • Removable Discontinuity

   $x=-8$

   $x=1$

   $x=9$

Source: Khan Academy, https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:discontinuities-of-rational-functions/e/points-of-discontinuity-of-rational-functions
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