Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 4 } { x + 3 }$
A) horizontal: $y = 4$; vertical: $x = - 3$
B) horizontal: $y = 3$; vertical: $x = 0$
C) horizontal: $x = - 3$; vertical: $y = - 4$
D) horizontal: $y = 0$; vertical: $x = - 3$
E) horizontal: $x = 0$; vertical: $y = - 3$

Question

Quizplus · Accepted Answer

The horizontal asymptote occurs as $x$ approaches infinity, and since the degree of the numerator is less than the degree of the denominator, $y = 0$. The vertical asymptote occurs where the denominator equals zero, which is at $x = -3$.

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