Key Concepts

• Boundary points are 1) solutions of the polynomial or rational equation AND 2) restrictions of the rational equation of the given inequality when it is available.
• When we plot the boundary points, solutions can be either open circles (if [latex]<[/latex] or [latex]>[/latex]) or closed circles (if [latex]\leq[/latex] or [latex]\geq[/latex]) based on the inequality sign of the given inequality while restrictions are always open circles.
• Any number in each interval could be a test value for the interval.
• If a test value makes the given inequality true, the interval is a solution of the inequality.