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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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