Inequalities can be represented graphically by drawing the graph, and shading in the appropriate region.
The four possibilities are:
- if the inequality is \(>\), draw the graph with a dotted line and shade in the region above the graph;
- if the inequality is \(<\), draw the graph with a dotted line and shade in the region below the graph;
- if the inequality is \(≥\), draw the graph with a solid line and shade in the region above the graph;
- if the inequality is \(≤\), draw the graph with a solid line and shade in the region below the graph.
The solutions to the inequality \(f(x) < g(x)\) are the values of \(x\) for which the graph \(y=f(x)\) is below the graph \(y=g(x)\).
The solutions to the inequality \(f(x) > g(x)\) are the values of \(x\) for which the graph \(y=f(x)\) is above the graph \(y=g(x)\).
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