Question

Determine the vertical asymptote for the rational function f(x) = x - 4 over 2x - 3

Answer 1

Answer:

x = $\frac{3}{2}$

Step-by-step explanation:

Given

f(x) = $\frac{x-4}{2x-3}$

The denominator cannot be zero as this would make f(x) undefined.

Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non zero for this value then it is a vertical asymptote.

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = $\frac{3}{2}$

Thus x = $\frac{3}{2}$ is the vertical asymptote