Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { x } { x - 4 }$ .
A)horizontal: y = 0 ; vertical: x = 4
B)horizontal: y = -4 ; vertical: x = 0
C)horizontal: x = 0; vertical: y = 4
D)horizontal: x = 4 ; vertical: y = -1
E)horizontal: y = 1 ; vertical: x = 4

Question

Quizplus · Accepted Answer

Horizontal asymptotes are found by examining the behavior of a function as $x$ approaches infinity. For $f(x) = \frac{x}{x-4}$, as $x$ approaches infinity, the function approaches $y = 1$, since the degrees of the numerator and denominator are the same and their leading coefficients are equal. Vertical asymptotes occur where the denominator of a fraction equals zero (and the numerator is not zero at that point), which for this function is at $x = 4$.

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