Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 4 } { x - 5 }$
A) horizontal: $y = 4$; vertical: $x = 5$
B) horizontal: $x = 0$; vertical: $y = 5$
C) horizontal: $y = - 5$; vertical: $x = 0$
D) horizontal: $x = 5$; vertical: $y = - 4$
E) horizontal: $y = 0$; vertical: $x = 5$

Question

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 4 } { x - 5 }$ 
A) horizontal: $y = 4$; vertical: $x = 5$
B) horizontal: $x = 0$; vertical: $y = 5$
C) horizontal: $y = - 5$; vertical: $x = 0$
D) horizontal: $x = 5$; vertical: $y = - 4$
E) horizontal: $y = 0$; vertical: $x = 5$

Quizplus · Accepted Answer

The horizontal asymptote occurs where the function approaches a y-value as x approaches infinity. For $f(x) = \frac{4}{x-5}$, as $x$ approaches infinity, the fraction approaches 0, so the horizontal asymptote is $y = 0$. The vertical asymptote occurs where the function is undefined, which is at $x = 5$, making the vertical asymptote $x = 5$.

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