Question

Can anyone explain how to determine whether f is continuous at c when c=2 and f(x)=x^3-3x^2+2x-6? I know it is continuous, but I don't know why.

Answer 1

This function is continuous as it is a cubic function as the leading term is to the power of three. Now , a cubic function does not have any breaks or gaps and it can take all x values. Hence, as it can take all x values, it is a continuous function.

Answer 2

Thank You so much! That makes way more sense!