Question

How do you graph `y<=(x+1)^3`?

Answer 1

Please see below.

Explanation:

The graph of `y=(x+1)^3` appears as below:
graph{(x+1)^3 [-10, 10, -5, 5]}

This divides Cartesian plane in three parts.

1. The curve itself which satisfies `y=(x+1)^3` and this is a part of solution as the desired graph `y<=(x+1)^3` includes equality.
2. Area to the left of it. One point `(-5,0)` lies in this part and for this we have `0>(-5+1)^3` and hence this point does not lie on the graph. So will other points to the left of curve.
3. Area to the right of it. One point `(0,0)` lies in this part and for which we have `0<(0+1)^3` and hence this point lies on the graph. So will other points to the right of the curve.

Hence solution is

graph{y<=(x+1)^3 [-10, 10, -5, 5]}

Note : If we had the inequality `y<(x+1)^3`, the line is not a solution and appears as dotted. The graph would be

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