Question

How is the function `1/9*x^3 +5, x<-3` not continuous at x=1 and what type of correspondence does it display?

Answer 1

Please see below.

Explanation:

For `f(x) = 1/9x^3+5`, for `x < -3`, the domain is `(-oo,-3)`

Therefore `f` is not defined at `x-1` so it cannot be continuous there.

Since `f'(x) = 1/3 x^2` is always positive, the function is a one to one correspondence.