question 5 · 2 points consider the graph of the function $f(x)=\frac{x^{2}+x - 12}{x^{2}-6x + 8}$. what are…

question 5 · 2 points consider the graph of the function $f(x)=\frac{x^{2}+x - 12}{x^{2}-6x + 8}$. what are the vertical asymptotes? list the $x$-values separated by commas. provide your answer below:

question 5 · 2 points consider the graph of the function $f(x)=\frac{x^{2}+x - 12}{x^{2}-6x + 8}$. what are the vertical asymptotes? list the $x$-values separated by commas. provide your answer below:

Answer

Explanation:

Step1: Factor the denominator

Factor $x^{2}-6x + 8=(x - 2)(x - 4)$.

Step2: Find values making denominator zero

Set $(x - 2)(x - 4)=0$. By the zero - product property, $x-2 = 0$ gives $x = 2$ and $x - 4=0$ gives $x = 4$. These are the values that make the denominator of $f(x)=\frac{x^{2}+x - 12}{x^{2}-6x + 8}$ zero while the numerator is non - zero at these points.

Answer:

$2,4$