question find all vertical asymptotes of the following function. f(x)=(x^2 + 8x - 9)/(2x^2 - 12x) answer…

question find all vertical asymptotes of the following function. f(x)=(x^2 + 8x - 9)/(2x^2 - 12x) answer attempt 1 out of 2 no vertical asymptotes no vertical asymptotes one vertical asymptote two vertical asymptotes

question find all vertical asymptotes of the following function. f(x)=(x^2 + 8x - 9)/(2x^2 - 12x) answer attempt 1 out of 2 no vertical asymptotes no vertical asymptotes one vertical asymptote two vertical asymptotes

Answer

Explanation:

Step1: Factor the numerator and denominator

The numerator $x^{2}+8x - 9=(x + 9)(x - 1)$. The denominator $2x^{2}-12x=2x(x - 6)$. So $f(x)=\frac{(x + 9)(x - 1)}{2x(x - 6)}$.

Step2: Find the values that make the denominator zero

Set the denominator equal to zero: $2x(x - 6)=0$. Solving $2x=0$ gives $x = 0$, and solving $x - 6=0$ gives $x=6$.

Step3: Check for removable discontinuities

There are no common factors between the numerator and denominator that can be canceled out. So the vertical - asymptotes occur at the values of $x$ that make the denominator zero.

Answer:

Two Vertical Asymptotes