Question

find all vertical asymptotes of the following function. f(x) = (5x² - 21x + 4)/(2x - 8) answer attempt 1 out of 2 no vertical asymptotes submit answer

Explanation:

Step1: Find the denominator's zero

Set the denominator \(2x - 8=0\). Solving for \(x\), we get \(2x=8\), so \(x = 4\).

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

Substitute \(x = 4\) into the numerator \(5x^{2}-21x + 4\).
\(5\times4^{2}-21\times4 + 4=5\times16-84 + 4=80-84 + 4=0\).
Since both numerator and denominator are zero at \(x = 4\), we factor the numerator.
Factor \(5x^{2}-21x + 4=(5x - 1)(x - 4)\).
So \(f(x)=\frac{(5x - 1)(x - 4)}{2(x - 4)}=\frac{5x - 1}{2}\), \(x
eq4\).

Answer:

No Vertical Asymptotes