Question

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

Answer 1

x =
`(3)/(2)`

Explanation:

Given

f(x) =
`(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 =
`(3)/(2)`

Thus x =
`(3)/(2)` is the vertical asymptote