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IB DP Maths: AI HL复习笔记2.2.2 Graphing Functions
Category:
IB课程
,
教材笔记
,
福利干货
Date: 2022年7月20日 上午11:49
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 G
DC
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
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 Example
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
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
转载自savemyexams
Previous post: IB DP Maths: AI HL复习笔记2.2.1 Functions
Next post: IB DP Maths: AI HL复习笔记2.2.3 Properties of Graphs
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