Reflections of Graphs (Edexcel IGCSE Maths A (Modular))
Revision Note
Reflections of Graphs
What are reflections of graphs?
Reflections of graphs are a type of transformation where the curve is reflected about one of the axes
How do I reflect graphs?
Let be the equation of the original graph
is a reflection in the -axis
The coordinates change sign
The coordinates are unaffected
is a reflection in the -axis
The coordinates change sign
The coordinates are unaffected
Any asymptotes of are also reflected
Exam Tip
When reflecting graphs in the exam, reflect any key points on the graph first, then join them up with a smooth curve.
How does a reflection affect the equation of the graph?
When a graph is reflected, you can change its equation algebraically
There is no need to sketch the graph
Reflecting in the -axis puts a in front of the whole equation
For example, becomes
This simplifies to
Reflecting in the -axis replaces any with in the equation
For example, becomes
This simplifies to
How do I apply a combined reflection?
The graph of is a combined reflection in both the and axes
It does not matter which order you apply these in
For example, reflect about the -axis then about the -axis
Worked Example
The diagram below shows the graph of .
Sketch the graph of .
The transformation is a reflection in the -axis
Reflect the points (-2, 6) and (1, -3) in the -axis to get (2, 6) and (-1, -3)
Sketch these points and join with a smooth curve through the origin
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