determine the points of discontinuity for the following rational function. y = (x + 5)/(x² + 8x + 15) what…

determine the points of discontinuity for the following rational function. y = (x + 5)/(x² + 8x + 15) what are the points of discontinuity? select all that apply. a. x = -5 b. y = 0 c. x = 0 d. x = -3 e. y = -3 f. y = -5 g. there are no points of discontinuity. help me solve this view an example get more help

determine the points of discontinuity for the following rational function. y = (x + 5)/(x² + 8x + 15) what are the points of discontinuity? select all that apply. a. x = -5 b. y = 0 c. x = 0 d. x = -3 e. y = -3 f. y = -5 g. there are no points of discontinuity. help me solve this view an example get more help

Answer

Answer:

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

Explanation:

Step1: Factor the denominator

$x^{2}+8x + 15=(x + 3)(x+5)$

Step2: Find values making denominator 0

Set $(x + 3)(x + 5)=0$. Then $x+3 = 0$ gives $x=-3$ and $x + 5=0$ gives $x=-5$. A rational function $y=\frac{f(x)}{g(x)}$ is discontinuous at values of $x$ for which $g(x)=0$. So the points of discontinuity are $x=-3$ and $x=-5$.