Question

multiple choice 1 point 19) what are all the vertical asymptotes of the graph of the following function? $y = \frac{2x^2 + 6x - 8}{x^2 - 2x - 15}$ a. $x = -3, x = 5$ b. $x = 3, x = -5$ c. $x = -4, x = 2$ d. $x = 4, x = -1$

Explanation:

Step1: Factor the denominator

$x^2 - 2x - 15 = (x-5)(x+3)$

Step2: Set denominator to 0

$(x-5)(x+3) = 0$

Step3: Solve for x

$x-5=0 \implies x=5$; $x+3=0 \implies x=-3$

Answer:

A. $x = - 3, x = 5$