Question

question 9 · 1 point
consider the graph of the function $f(x) = \frac{x^2 - 3x - 4}{x^2 - 6x + 8}$.
what are the vertical asymptotes? list the $x$-values separated by commas.
provide your answer below:
$x = \square$

Explanation:

Step1: Factor denominator

Denominator: $x^2 - 6x + 8 = (x-2)(x-4)$
Set to zero: $(x-2)(x-4)=0 \Rightarrow x=2,4$

Step2: Check numerator at these x-values

Numerator: $x^2 - 3x - 4 = (x-4)(x+1)$
At $x=2$: $(2-4)(2+1)=(-2)(3)=-6
eq 0$
At $x=4$: $(4-4)(4+1)=0 \cdot 5=0$ (canceled factor)

Answer:

2