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AQA A Level Maths: Pure复习笔记2.9.3 Reflections
Category:
A-level课程
,
教材笔记
,
福利干货
Date: 2022年7月27日 下午5:02
Reflections
What are graph transformations?
When you alter a function in certain ways, the effects on the graph of the function can be described by geometrical transformations
With a reflection all the points on the graph are reflected in either the x or the y
Any
asymptotes
of f(x) are also affected by the reflection (reflect them as you would reflect the function of a straight line)
If an asymptote is one of the coordinate axes, or is perpendicular to the coordinate axis in which the graph is reflected, it will not be affected
What do I need to know about graph reflections?
The graph of y = -f(x) is a reflection in the x axis
The x coordinates of points stay the same; y coordinates have their signs flipped (positive to negative, negative to positive)
Points on the x axis stay where they are
All other points are reflected to the other side of the x axis
The graph of y = f(-x) is a reflection in the y axis
The y coordinates of points stay the same; x coordinates have their signs flipped (positive to negative, negative to positive)
Points on the y axis stay where they are
All other points are reflected to the other side of the y axis
Any
asymptotes
of f(x) are also affected by the reflection (reflect them as you would reflect the function of a straight line)
If an asymptote is one of the coordinate axes, or is perpendicular to the coordinate axis in which the graph is reflected, it will not be affected
Worked Example
转载自savemyexams
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Next post: AQA A Level Maths: Pure复习笔记2.10.1 Combinations of Transformations
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