Question

find the vertical asymptotes (if any) of the graph of the function $f(x)=\frac{x^{2}}{x^{2}-9}$

Explanation:

Step1: Factor denominator

\( x^2 - 9 = (x - 3)(x + 3) \)

Step2: Find undefined points

Set \( (x - 3)(x + 3) = 0 \), so \( x = 3 \), \( x = -3 \)

Step3: Check numerator at these points

Numerator \( x^2 \) at \( x = 3 \): \( 3^2 = 9
eq 0 \); at \( x = -3 \): \( (-3)^2 = 9
eq 0 \)

Answer:

The vertical asymptotes are \( x = -3 \) and \( x = 3 \)