Vertical Asymptotes & Holes of Rational Functions

Amber Taylor, Arlene Bustamante, Mya Warren

Definition(s): Vertical Asymptotes- vertical asymptotes are vertical lines which correspond with the zeros of the denominator of a rational function

Hole- empty space

Find the vertical asymptote(s) and hole(s) of the following function, if any.

Example 1: STEP 1: Factor both the numerator and denominator

                      STEP 2: Cross out the "like terms" whatever you cross out is the "hole"

                      STEP 3: The factor that is left on the bottom is the vertical asymptote

Find the vertical asymptote(s) and hole(s) of the following function, if any.

Example 2: Step 1: Set the denominator equal to zero, this is your vertical asymptote

Example 2 (continued): Step 2: Factor the constant, the only factors of five are positive/negative 1 and 5 and neither of those equal -3 so therefore since the numerator can't be factored there is no "hole"

Find the vertical asymptote(s) and hole(s) of the following function, if any.

Example 3: STEP 1: Factor out the numerator and put that over the original denominator then you will see that there are two like terms cross them out and that's your "hole".

                       STEP 2: There isn't a factor left on the bottom so therefore you do not have any vertical asymptotes

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