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The following graph identifies the region(s) that would make the polynomial inequality true.
Example 7: Graph Solution
The graph of f(x) = x3 - x2 - 2x is shown below - again, this is the graph of f(x).
The red region(s) above the x-axis are the x-solutions for the inequality x3 - x2 - 2x ≥ 0.
This would include all x values between and including x = -1
and x = 0, and also all x values greater or equal to 2 to infinity.
Read Q1 and its answer before proceeding to the next paragraph.
Q1: Now, look at the red and white regions of the function's graph, f(x) = x3 - x2 - 2x.
What can you determine must be true about the function's graph (that is, its behavior) around the zeros? What are the red and white areas telling us? Could it be the solution set(s)?
A1: If the region between the zeros is negative (white region), then the function's graph is below the x-axis. If the region between the zeros is positive (red region), then the function's graph is above the x-axis.
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