Inequalities on Graphs (Cambridge International A-Level Mathematics)

Inequalities on graphs

What are inequalities on graphs?

• Inequalities can be represented on graphs by shaded regions and dotted or solid lines

• These inequalities have two variables, x and y
• Several inequalities are used at once
• The solution is an area on a graph (often called a region)
• The inequalities can be linear or quadratic

How do I draw inequalities on a graph?

• Sketch each graph

  • If the inequality is strict (< or >) then use a dotted line
  • If the inequality is weak (≤ or ≥) then use a solid line

• Decide which side of the line satisfies the inequality

  • Choose a coordinate on each side and test it in the inequality

    • The origin is an easy point to use

  • If it satisfies the inequality then that whole side of the line satisfies the inequality

    • For example: (0,0) satisfies the inequality y < x² + 1 so you want the side of the curve that contains the origin

Exam Hint

• Recognise this type of inequality by the use of two variables
• You may have to deduce the inequalities from a given graph
• Pay careful attention to which region you are asked to shade
• Sometimes the exam could ask you to shade the region that satisfies the inequalities, this means you should shade the region that is wanted
• As long as your final answer is clear you should get the marks!

Worked Example