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IBMathsDPApplications & Interpretation (AI)SLRevision Notes2. FunctionsFurther Functions & GraphsIntersecting Graphs

Intersecting Graphs (DP IB Applications & Interpretation (AI)): Revision Note

Dan Finlay

Written by: Dan Finlay

Reviewed by: Mark Curtis

Updated on

DP Applications & Interpretation (AI): SLDP Analysis & Approaches (AA): HLDP Analysis & Approaches (AA): SLDP Applications & Interpretation (AI): HLDP Applications & Interpretation (AI): HLDP Applications & Interpretation (AI): SLDP Analysis & Approaches (AA): HLDP Analysis & Approaches (AA): SL

Intersecting graphs

How do I find the points of intersection between two graphs?

  • Plot both graphs on your GDC

    • then use the intersect function to find the coordinates of the points of intersection

Examiner Tips and Tricks

You may have to adjust the scales or zoom to see all points of intersection on your GDC.

  • The coordinates of the points of intersection

    • are solutions to simultaneous equations

Graph showing lines 2x-y=3 and 3x+y=7 intersecting at point (2,1) on axes. Caption states solving simultaneously gives x=2, y=1.

How can I use graphs to solve equations?

  • To solve space f left parenthesis x right parenthesis equals a

    • Plot the two graphs space y equals f left parenthesis x right parenthesis and space y equals a on your GDC

    • Find the points of intersection

      • The x-coordinates are the solutions of space f left parenthesis x right parenthesis equals a

  • To solve space f left parenthesis x right parenthesis equals g left parenthesis x right parenthesis

    • Plot the two graphs space y equals f left parenthesis x right parenthesis and space space y equals g left parenthesis x right parenthesis on your GDC

    • Find the points of intersections

    • The x-coordinates are the solutions of space f left parenthesis x right parenthesis equals g left parenthesis x right parenthesis

Examiner Tips and Tricks

Exam questions can ask for just the number of solutions (rather than finding each solution), which is equal to the number of points of intersection.

Worked Example

Two functions are defined by

space f left parenthesis x right parenthesis equals x cubed minus x and space g left parenthesis x right parenthesis equals 4 over x.

(a) Sketch the graph of space y equals f left parenthesis x right parenthesis.

2-2-2-ib-ai-sl-intersecting-graphs-a-we-solution

(b) Write down the number of real solutions to the equation space x cubed minus x equals 2.

2-2-2-ib-ai-sl-intersecting-graphs-b-we-solution

(c) Find the coordinates of the points where space y equals f left parenthesis x right parenthesis and space y equals g left parenthesis x right parenthesis intersect.

2-2-2-ib-ai-sl-intersecting-graphs-c-we-solution

(d) Write down the solutions to the equation space x cubed minus x equals 4 over x.

2-2-2-ib-ai-sl-intersecting-graphs-d-we-solution

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    Author
    Reviewer
    Dan Finlay

    Author: Dan Finlay

    Expertise: Maths Subject Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

    Mark Curtis

    Reviewer: Mark Curtis

    Expertise: Maths Content Creator

    Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.