The vertical asymptotes of a function corresponds to the zeros of the denominator of the function.
The vertical asymptotes are: x = 4 and x = -4
The function is given as:
[tex]\mathbf{f(x) = \frac{3x}{x^2 - 16}}[/tex]
Equate the denominator to 0
[tex]\mathbf{x^2 - 16 = 0}[/tex]
Express 16 as 4^2
[tex]\mathbf{x^2 - 4^2 = 0}[/tex]
Express as difference of two squares
[tex]\mathbf{(x - 4)(x + 4) = 0}[/tex]
Split
[tex]\mathbf{(x - 4) = 0\ or\ (x + 4) = 0}[/tex]
Solve for x
[tex]\mathbf{x = 4\ or\ x = -4}[/tex]
Hence, the vertical asymptotes are: x = 4 and x = -4
Read more about vertical asymptotes at:
https://brainly.com/question/4084552
