Answer
See graph below.
Work Step by Step
The question asks to graph the solution set of the system of inequalities.
Here are some criteria for graphing inequalities:
1. If it is $\lt$ or $\gt$, then the graph must be dashed.
2. If it is $\leq$ or $ \geq$, then the graph must be solid.
3. If it is $\lt$ or $\leq$ (with y being isolated), then the shading is below, left, or inside the graph.
4. If it is $\gt$ or $\geq$ (with y being isolated), then the shading is above, right, or outside the graph.
Given:
1. $y \geq x^3$
2. $y \leq 2x + 4$
3. $x + y \geq 0$
Graph $y = x^3$, $y = 2x + 4$, and $y = -x$ with a solid line.
Equation 1 and 3 is $\geq$, so the shading will be above the graph, respectively.
Equation 2 is $\leq$, so the shading will be below the graph.
The solution set is where the red, blue, and purple areas overlap (the answer is the dark purple area ).
See graph below.
This solution set is bounded.
