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]}