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

1 Answer
Feb 24, 2018

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]}