Transformations of Graphs
Maths: Edexcel IGCSE Higher, topic 3.4.2
Translations
Translations are when we move a graph without changing its shape.
,w_800.png)
Vertical translation
- Moves a function up or down. For y = f(x):
- y = f(x) + a moves the graph up by a
- y = f(x) - a moves the graph down by a
,w_800.png)
Horizontal translation
- Moves a function left or right. For y = f(x):
- y = f(x + a) moves the graph left by a
- y = f(x - a) moves the graph right by a
Reflections
,w_800.png)
Reflection in the x axis
- For a function y = f(x):
- y = -f(x) gives a reflection in the x axis
,w_800.png)
Reflection in the y axis
- For a function y = f(x):
- y = f(-x) gives a reflection in the y axis
,w_800.png)
Invariant points
- Invariant points are points that don’t change in a transformation (e.g reflection).
- (0, 1.5) is the invariant point shown in the above reflection.
Stretches and Compressions
Graphs of functions can be stretched or compressed in either the horizontal or vertical direction.
Vertical stretches and compressions
- Given a function f(x), a new function g(x) = af(x), where a is a constant, is a vertical stretch or vertical compression of the function f(x).
- If a > 1, then the graph will be stretched.
- If 0 < a < 1, then the graph will be compressed.
Vertical stretches and compressions
Horizontal stretches and compressions
- Given a function f(x), a new function g(x) = f(bx), where b is a constant, is a horizontal stretch or horizontal compression of the function f(x).
- If b > 1, then the graph will be compressed by .
- If 0 < b < 1, then the graph will be stretched by .
Horizontal stretches and compressions
Test yourself on Transformations of Graphs
The equation of the blue line is x³ + 4. What colour line is (x - 2)³ + 4?
The equation of the blue line is x³ + 4. What colour line is (x + 2)³ + 4?
If y = f(x), where will y = f(x) + 7 appear on the same graph?
If y = f(x), where will y = f(x-3) appear on the same graph?
If y = f(x), where will y = f(x-2) - 8 appear on the same graph?