Question

Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?y > x2 – 1y ≤ –x2 + 4

Answer 1

For the graph y > x² - 1, since it uses the inequality "greater than (>) ", use a dashed line instead and shade the upper portion of the graph

For the graph y ≤ -x² + 4, since it uses the inequality "less than or equal to (≤)", use a solid line, and shade the lower portion of the graph.

This will result to the following graphs

The intersection of the shaded region of the two graphs is the solution set for the system of inequality.