find all vertical asymptotes of the following function\n$f(x)=\\frac{2x - 4}{5x - 6}$
find all vertical asymptotes of the following function\n$f(x)=\\frac{2x - 4}{5x - 6}$
Answer
Explanation:
Step1: Recall the definition of vertical asymptote
A vertical asymptote occurs at the value of (x) that makes the denominator of a rational function equal to zero (while the numerator is not zero at that value). For the function (f(x)=\frac{2x - 4}{5x-6}), we set the denominator equal to zero.
Step2: Solve the equation for the denominator
Set (5x - 6=0). Add (6) to both sides: (5x=6). Divide both sides by (5): (x = \frac{6}{5}). Check if the numerator is zero at (x=\frac{6}{5}). Substitute (x=\frac{6}{5}) into the numerator (2x - 4): (2\times\frac{6}{5}-4=\frac{12}{5}-\frac{20}{5}=-\frac{8}{5}\neq0).
Answer:
The vertical asymptote is (x = \frac{6}{5}).