Question

How do you graph the function `f(x)=(x-3)^3+4` and its inverse?

Answer 1

See below

Explanation:

First, visualise the curve of `y=(x-3)^3`, which is a simple positive cubic which intercepts the `x` axis at `x=3`:

graph{(x-3)^3 [-10, 10, -5, 5]}

Now, translate this curve upwards by 4 units:

graph{(x-3)^3+4 [-10, 10, -5, 5]}

And to find the inverse, simply reflect in the line `y=x`:

graph{(x-4)^(1/3)+3 [-10, 10, -5, 5]}