Question

What type of discontinuity exists for f(x) at x = 1?

Answer 1

f(x) = {5x^3 - 5 if x does not equal 1
{5 if x = 1

Answer 2

hmmm a graph would show it methinks
bear in mind that \(\bf 5x^3-5\implies 5(x^3-1)\)
which is just \(x^3\) with a 5 multiplier, making it narrower and a vertical shift down by 1

Answer 3

@HolsterEmission

Answer 4

Looking at this system of equations -->
If you were to graph it:

There is a hole at x=1 for f(x)=5x^3-5 but a closed hole at x=5 for yf(x)=5