question\nfind all vertical asymptotes of the following function.\n f(x)=\frac{9 x^{2}-25}{2 x-8} \nanswer…

question\nfind all vertical asymptotes of the following function.\n f(x)=\frac{9 x^{2}-25}{2 x-8} \nanswer attempt 1 out of 2\n

question\nfind all vertical asymptotes of the following function.\n f(x)=\frac{9 x^{2}-25}{2 x-8} \nanswer attempt 1 out of 2\n

Answer

Explanation:

Step1: Find the denominator zero

Set the denominator (2x - 8=0). Solve the equation (2x-8 = 0), we get (x = 4).

Step2: Check if the numerator is zero at (x = 4)

Substitute (x = 4) into the numerator (9x^{2}-25), we have (9\times4^{2}-25=9\times16 - 25=144 - 25=119\neq0).

Since the denominator is zero at (x = 4) and the numerator is non - zero at (x = 4), the function (y=\frac{9x^{2}-25}{2x - 8}) has a vertical asymptote at (x = 4).

Answer:

One Vertical Asymptote