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Unformatted text preview: Graph y = −x 2 .
1
Graph y = 5 −
.
x +2
√
Graph y = 1 − x + 7. Outline Basic Functions Translations Reﬂections Scaling General Transformations Scaling Suppose y = f (x ) is function and c > 0 is a constant.
If c > 1, then the graph of y = cf (x ) is the graph of
y = f (x ) stretched vertically by a factor of c .
If c < 1, then the graph of y = cf (x ) is the graph of
y = f (x ) compressed vertically by a factor of c .
If c > 1, then the graph of y = f (cx ) is the graph of
1
y = f (x ) compressed horizontally by a factor of c .
If c < 1, then the graph of y = f (cx ) is the graph of
1
y = f (x ) stretched horizontally by a factor of c . Outline Basic Functions Examples Example 3 1
Graph y = x .
3
2
Graph y = .
x
√
Graph y = 2x . 4 Graph e x /4 . 1 2 Translations Reﬂections Scaling General Transformations Outline Basic Functions Translations Reﬂections Scaling General Transformations General Transformations If f is a function and a, b , h, and k are real numbers, then
g (x ) = af (b (x − h)) + k
is the graph of f :
Translated vertically k units.
Translated horizontally h units.
Reﬂected across the x axis if a < 0.
Scaled vertically by a factor of a.
Reﬂected across the y axis if b < 0.
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Scaled horizontally by a factor of b . Outline Basic Functions Translations Reﬂections Scaling General Transformations Multiple Transformations When doing multiple transformations, proceed in the order of
operation.
In particular, scaling and reﬂecting take precedence over shifts.
Example
1 2 3 √
Graph y = 3 x + 1.
2
Graph y =
.
1−x
Graph y = (2 − 6x )1/3 ....
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 Spring '14
 K.JPlatt
 Algebra, Transformations

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