Question

What are the discontinuities of the function f(x) = the quantity x squared minus 36 over the quantity 4x plus 24?

Answer 1

there is a point discontinuity ( hole ) at (- 6, - 3 )

factor the numerator/denominator

f(x) =
`((x-6)(x+6))/(4(x+6))`

the factor (x + 6) cancels leaving the simplified version of f(x)

f(x) =
`(x-6)/(4)`

the removal of the factor (x + 6) from the numerator/denominator means there is a discontinuity at x + 6 = 0 , that is x = - 6

f(- 6 ) =
`(-6-6)/(4)` = - 3

there is a point discontinuity ( hole ) at (- 6, - 3 )