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 vertical asymptote occurs where the denominator is zero, which is at $x = 5$, and the horizontal asymptote for a rational function of this form is $y = 0$ since the degree of the numerator and denominator are the same and the leading coefficients result in a horizontal asymptote at $y = 0$.

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