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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

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

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

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

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

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

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

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