Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 1 } { x - 5 }$ .
A)horizontal: y = 1; vertical: x = 5
B)horizontal: x = 0; vertical: y = 5
C)horizontal: y = -5; vertical: x = 0
D)horizontal: x = 5; vertical: y = -1
E)horizontal: y = 0; vertical: x = 5

Question

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 1 } { x - 5 }$ .
A)horizontal: y = 1; vertical: x = 5
B)horizontal: x = 0; vertical: y = 5 
C)horizontal: y = -5; vertical: x = 0
D)horizontal: x = 5; vertical: y = -1
E)horizontal: y = 0; vertical: x = 5

Quizplus · Accepted Answer

The horizontal asymptote of $f(x) = \frac{1}{x-5}$ is y = 0, as x approaches infinity, the function approaches 0. The vertical asymptote is x = 5, where the function is undefined.

Determine the Equations of the Vertical and Horizontal Asymptotes of the Graph