Chapter 11, Problem 9MCQ

To determine

To identify: The asymptotes of the function

Answer to Problem 9MCQ

The function has vertical asymptote at $x=4$ and horizontal asymptote at $y=0$

Explanation of Solution

Given:

  $y=\frac{2}{x-4}$

Calculation:

A rational function in the form $y=\frac{a}{x-b}+c,a\ne 0$ has a vertical asymptote at $x-value$ that makes the denominator equal to zero, $x=b$

It has a horizontal asymptote at $y=c$

From the function it is seen that it has a vertical asymptote at $x=4$ and horizontal asymptote at $y=0$

Conclusion:

Hence, the function has vertical asymptote at $x=4$ and horizontal asymptote at $y=0$