3.7 Transformation of Functions

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3.7 Transformation of Functions
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1) Investigating y f(x p)
(4, 2)
(0, 2)
(left 4 units)
(7, 2)
(right 3 units)
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2) Investigating y f(x) q
(4, 2)
(4, 5)
(up 3 units)
(4, 3)
(down 5 units)
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3) Investigating y af(x)
(4, 2)
(4, 4)
(vertical stretch by 2)
(4, 1)
(vertical stretch by one-half)
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3) Investigating y af(x)
(4, 2)
(4, 2)
(inverted)
(4, 4)
(inverted stretch)
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4) Investigating y af(x p) q
(4, 2)
(1, 2)
left 5
(1, 4)
2
(1, 1)
down 3
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5) Investigating y f(kx)
(4, 2)
(2, 2)
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y af k(x p) q
- Shift right p units
y af k(x p) q
- Vertical stretch by a factor of a
- Vertical shift by a factor of q
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If the graph of f is given as y x3, describe
the transformations that you would apply to
obtain the following
a) y (x 1)3
left 1
b) y x3 2
down 2
vertical stretch 2 and reflection in the x-axis
c) y 2x3
horizontal stretch by a factor of 1/3 and a
reflection in the y-axis,
d) y ( 3x)3
right 5 and a vertical stretch by a factor of 2
e) y 2(x 5)3
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Example Given the ordered pair
(3, 5) belongs to g.
List the ordered pairs that correspond to
a) y 2g(x)
(3, 10)
Vertical stretch 2
b) y g(x) 4
(3, 9)
Up 4
c) y g(x 3)
(6, 5)
Right 3
(1.5, 5)
d) y g(2x)
Horizontal stretch 1/2
Reflect in the x-axis
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If the graph of f is given as , describe
the transformations that you would apply to
obtain the following
right 3
up 4
horizontal stretch 1/2
reflection in the x-axis
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Describe the transformations that you would apply
to f(x) to obtain the following
a) f(2x 6)
Left 3
f 2(x 3)
Horizontal stretch by a factor of 1/2.
b) f( 3x 12) 5
Right 4
Horizontal stretch by a factor of 1/3.
f3(x 4) 5
Reflection in y-axis
Up 5
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Describe the transformation on f (x)
f(x)






2x3
x3
Vertical stretch
Left 2, reflection in the x-axis
x4
(x 3)4
Right 3
Horizontal stretch, inverted
(x 1)2 4
x2
Left 1, up 4
Horizontal stretch (2), vertical stretch (0.5).
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The graph of y f(x) is given
Sketch the graph of
y f (2x6) 1
y f 2(x3) 1
Input output diagram
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reflect in x-axis
left 3
up 1
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y f 2(x 3) 1
2
left 3
reflect in x-axis
up 1
P(3, 2)
left 3
P
Q
R
(6, 2)
2
(3, 2)
reflect in x-axis
S
(3, 2)
up 1
P
P(3, 3)
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y f 2(x 3) 1
2
left 3
reflect in x-axis
up 1
Q(0, 2)
left 3
P
Q
R
(3, 2)
2
(1.5, 2)
reflect in x-axis
S
(1.5, 2)
up 1
Q
P
Q(1.5, 1)
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y f 2(x 3) 1
2
left 3
reflect in x-axis
up 1
R(3, 2)
left 3
P
Q
R
(0, 2)
2
(0, 2)
reflect in x-axis
S
(0, 2)
R
up 1
Q
P
R(0, 1)
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y f 2(x 3) 1
2
left 3
reflect in x-axis
up 1
S(4, 0)
left 3
P
Q
R
(1, 0)
2
(0.5, 0)
S
reflect in x-axis
S
(0.5, 0)
R
up 1
Q
P
S(0.5, 1)