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IB DP Maths: AI SL復習筆記2.2.2 Graphing Functions

Category: IB課程, 教材筆記, 福利干貨 Date: 2022年7月19日 上午11:02

Graphing Functions

How do I graph the function?y?=?f(x)?

What is the difference between “draw” and “sketch”?

  • If asked to sketch you should:
    • Show the general shape
    • Label any key points such as the intersections with the axes
    • Label the axes
  • If asked to draw you should:
    • Use a pencil and ruler
    • Draw to scale
    • Plot any points?accurately
    • Join points with a straight line or smooth curve
    • Label any key points such as the intersections with the axes
    • Label the axes

How can my GDC help me sketch/draw a graph?

  • You use your GDC to plot the graph
    • Check the scales on the graph to make sure you see the full shape
  • Use your GDC to find any key points
  • Use your GDC to check specific points to help you plot the graph

Key Features of Graphs

What are the key features of graphs?

  • You should be familiar with the following key features and know how to use your GDC to find them
  • Local minimums/maximums
    • These are points where the graph has a minimum/maximum for a small region
    • They are also called?turning points
    • A graph can have multiple local minimums/maximums
    • A local minimum/maximum is not necessarily the minimum/maximum of the whole graph
      • This would be called the?global?minimum/maximum
    • For quadratic graphs the minimum/maximum is called the?vertex
  • Intercepts
    • y--?– intercepts are where the graph crosses the?y-axis
      • At these points?x?= 0
    • x?– intercepts are where the graph crosses the?x-axis
      • At these points?y?= 0
      • These points are also called the?zeros of the function?or?roots of the equation
  • Symmetry
    • Some graphs have lines of symmetry
      • A quadratic will have a vertical line of symmetry
  • Asymptotes
    • These are lines which the graph will get closer to but not cross
    • These can be horizontal or vertical
      • Exponential graphs have horizontal asymptotes
      • Graphs of variables which vary inversely can have vertical and horizontal asymptotes

2.7.1-Sketching-Polynomials-Notes-Diagram-1

Exam Tip

  • Most GDC makes/models will not plot/show asymptotes just from inputting a function
    • Add the asymptotes as additional graphs for your GDC to plot
    • You can then check the equations of your asymptotes visually
    • You may have to zoom in or change the viewing window options to confirm an asymptote
  • Even if using your GDC to plot graphs and solve problems sketching them as part of your working is good exam technique
    • Label the key features of the graph and anything else relevant to the question on your sketch

Worked Example2-2-2-ib-ai-key-features-of-graphs-a-we-solution

2-2-2-ib-ai-key-features-of-graphs-b-we-solution

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

2.7.3-Solving-Equations-Graphically-Notes-Diagram-1

How can I use graphs to solve equations?

Exam Tip

  • 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

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

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


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

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

 

 

 

 

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