Question

give the equations of any vertical, horizontal, or oblique asymptotes for the graph of the rational function $f(x)=\frac{2}{x - 5}$. the vertical asymptote(s) is(are) $x = square$. (use a comma to separate answers as needed.)

Explanation:

Step1: Find vertical asymptote

Set denominator equal to 0.
$x - 5=0$

Step2: Solve for x

$x = 5$

Step3: Find horizontal asymptote

Degree of numerator is 0, degree of denominator is 1. When degree of numerator < degree of denominator, horizontal asymptote is $y = 0$.
There is no oblique asymptote as degree of numerator < degree of denominator.

Answer:

Vertical asymptote: $x = 5$
Horizontal asymptote: $y = 0$
No oblique asymptote.