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

1 Answer
Jul 30, 2018

Answer:

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]}