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Slide 1

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Transforming graphs of functions
Graphs can be transformed by shifting & stretching them.
The equation of the transformed graph will be related to the
equation of the original graph.
When investigating transformations it is most useful to express
functions using function notation.
For example, suppose we wish to investigate transformations
of the function f(x) = x2.
The equation of the graph of y = x2, can be written as y = f(x).…read more

Slide 2

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Vertical translations
Here is the graph of y = x2, where y = f(x).
y This is the graph of y = f(x) + 1
and this is the graph of y = f(x) + 4.
The graph of y = f(x) + a is the graph
of y = f(x) translated by the vector 0 .
a
x
This is the graph of y = f(x) ­ 3
and this is the graph of y = f(x) ­ 7.
The graph of y = f(x) - a is the graph of
y = f(x) translated by the vector 0
.
-a…read more

Slide 3

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Horizontal translations
Here is the graph of y = x2 ­ 3, where y = f(x).
y This is the graph of y = f(x ­ 1),
and this is the graph of y = f(x ­ 4).
The graph of y = f(x + a ) is the graph
of y = f(x) translated by the vector ­a .
0
x
This is the graph of y = f(x + 2),
and this is the graph of y = f(x + 3).
The graph of y = f(x - a ) is the graph
of y = f(x) translated by the vector +a .
0…read more

Slide 4

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Reflections in the x-axis
Here is the graph of y = x2 ­2x ­ 2, where y = f(x).
y
This is the graph of y = ­f(x).
The graph of y = ­f(x) is the graph of
x
y = f(x) reflected in the x-axis.…read more

Slide 5

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Reflections in the y-axis
Here is the graph of y = x3 + 4x2 ­ 3 where y = f(x).
y
This is the graph of y = f(­x).
The graph of y = f(­x) is the graph of
x y = f(x) reflected in the y-axis.…read more

Slide 6

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Stretches in the y-direction
30 y = f(x)
y co-ordinates
tripled
3f(x)
20
2f(x) y co-ordinates
doubled
10 f(x)
x
-6 -4 -2 0 2 4 6 8
0
Points located on the
The graph of kf -10
x axis remain fixed.
(x) gives a
stretch of f(x) by
scale factor k in -20
the y direction. kf(x)
-30…read more

Slide 7

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Slide 8

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Slide 9

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Comments

Nicobigboy

davie where u at?

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