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

Dan Finlay

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

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Intersecting Graphs

How do I find where two graphs intersect?

  • Plot both graphs on your GDC

  • Use the intersect function to find the intersections

  • Check if there is more than one point of intersection

Solving Equations Graphically Notes Diagram 1

How can I use graphs to solve equations?

  • One method to solve equations is to use graphs

  • 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 intersections

    • The x-coordinates are the solutions of the equation

  • 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 the equation

  • Using graphs makes it easier to see how many solutions an equation will have

Examiner Tips and Tricks

  • You can use graphs to solve equations

    • Questions will not necessarily ask for a drawing/sketch or make reference to graphs

    • Use your GDC to plot the equations and find the intersections between the graphs

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 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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    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.