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

Feb 24, 2018

See below

#### Explanation:

First, visualise the curve of $y = {\left(x - 3\right)}^{3}$, 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]}