Math 1650 Lecture Notes
§2.4
Jason Snyder, PhD.
Transformations of Functions
Page
1
of
8
§
2.4: Transformations of Functions
Vertical Shifting
Adding a constant to a function shifts its graph vertically: upward if the constant
is positive and downward if the constant is negative.
Example 1
Vertical Shifts of Graphs
Use the graph of
? ?
=
?
2
to sketch the graph of each function.
(a)
? ?
=
?
2
+ 2
(b)
? ?
=
?
2
−
3
x
y
Vertical Shifts of Graphs
Suppose c > 0.
To graph
?
=
? ?
+
𝑐
, shift the graph of
?
=
? ?
upward c units.
To graph
?
=
? ? − 𝑐
, shift the graph of
?
=
? ?
downward c units.
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Math 1650 Lecture Notes
§2.4
Jason Snyder, PhD.
Transformations of Functions
Page
2
of
8
Example 2
Vertical Shifts of Graphs
Use the graph of
? ?
=
?
3
−
5
?
, which is sketched below, to sketch the graph of
each of the following.
(a)
? ?
=
?
3
−
5
?
+ 3
(b)
? ?
=
?
3
−
5
? −
2
x
y
Horizontal Shifting
Suppose we have the graph of
?
=
?
(
?
)
, how would we use this graph to sketch
the graphs of
?
=
?
(
?
+
𝑐
)
and
?
=
? ? − 𝑐
, where c > 0?
The
y
value of
?
(
? − 𝑐
)
is the same as
?
(
?
)
evaluated at
x
–
c
.
Since
x
–
c
is c
units to the left of
x
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 Spring '06
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 Math, Calculus, Binary relation, Even and odd functions, Jason Snyder

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