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

Jul 30, 2018

#### Explanation:

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

This divides Cartesian plane in three parts.

1. The curve itself which satisfies $y = {\left(x + 1\right)}^{3}$ and this is a part of solution as the desired graph $y \le {\left(x + 1\right)}^{3}$ includes equality.
2. Area to the left of it. One point $\left(- 5 , 0\right)$ lies in this part and for this we have $0 > {\left(- 5 + 1\right)}^{3}$ 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 $\left(0 , 0\right)$ lies in this part and for which we have $0 < {\left(0 + 1\right)}^{3}$ 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 $y < {\left(x + 1\right)}^{3}$, the line is not a solution and appears as dotted. The graph would be

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