Question

Find all vertical asymptotes of the following function

Answer 1

x = - 4

Explanation:

f(x) =
`(2x^2-8)/(x+4)`

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.

x + 4 = 0 ( subtract 4 from both sides )

x = - 4 ← excluded value

2x² - 8 = 2(- 4)² - 8 = 32 - 8 = 24 ← non zero numerator

then x = - 4 is the vertical asymptote of f(x)