Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { x } { x - 3 }$ .
A)horizontal: $x = 0$ ; vertical: $y = 3$
B)horizontal: $y = - 3$ ; vertical: $x = 0$
C)horizontal: $y = 1$ ; vertical: $x = 3$
D)horizontal: $y = 0$ ; vertical: $x = 3$
E)horizontal: $x = 3$ ; vertical: $y = - 1$

Question

Quizplus · Accepted Answer

The horizontal asymptote is found by dividing the leading coefficients of the numerator and denominator, which gives $y = 1$. 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