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## Transformations of Functions

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### Mathematics Enrichment. through Technology. Graphing. Given the following function, If: a 0, then shift the graph 'a' units up. If: a 0, then shift the graph 'a' ... – PowerPoint PPT presentation

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Title: Transformations of Functions

1
Transformations of Functions
• Viviana C. Castellón
• East Los Angeles College
• MEnTe
• Mathematics Enrichment
• through Technology

2
Graphing
3
• Given the following function,
• If a gt 0, then shift the graph a units up
• If alt0, then shift the graph a units down

4
• Given the following function,
• Since a gt 0, then the graph will be
• shift up 5 units

5
Lets Graph
6
• Given the following function,
• How will the graph look?

7
Lets Graph
8
• Given the following function,
• Since a lt 0, then the graph will be
• shift down 3 units

9
Lets Graph
10
• Given the following function,
• How will the graph look?

11
Lets Graph
12
Given the following function
• For this equation, b is inside the square root.
• We get the expression and equal it to zero.
• If b gt 0, then shift the graph b
• units right
• If b lt 0, then shift the graph b
• units left

13
• Given the following function,
• We get the expression and equal it to zero.
• Since b lt 0, then shift the graph
• 2 units left

14
Lets Graph
15
• Given the following function,
• How will the graph look?

16
Lets Graph
17
• Given the following function,
• How will the graph look?

18
Lets Graph
19
• Given the following function,
• How will the graph look?

20
Lets Graph
21
• Recall
• a gt 0 then shift up
• a lt 0 then shift down
• Equal the expression to zero
• b gt 0 then shift to the right
• b lt 0 then shift to the left

22
• Given the following function,
• How will the graph look?

23
Lets Graph
24
• Given the following function,
• How will the graph look?

25
Lets Graph
26
• Given the following function,
• How will the graph look?

27
Lets Graph
28
• Given the following function,
• How will the graph look?

29
Lets Graph
30
Given the following function,
For this equation, c determines how wide or thin
half of the parabola will be. if cgt1, then the
graph is closer to the y-axis if c1, then the
graph remains the same if 0ltclt1, then the
graph is further from the y-axis if c is a
negative number, then the graph will reflect on
the x-axis
31
Lets Graph
32
Lets Graph
33
Lets Graph
34
• Recall
• agt0 then shift up
• alt0 then shift down
• Equal the function to zero
• bgt0 then shift to the right
• blt0 then shift to the left
• if cgt1, then the graph is closer to the y-axis
• if c1, then the graph is the same
• if 0ltclt1, then the graph is further from the
y-axis

35
• Given the following function,
• How will the graph look?

36
Lets Graph
37
• Given the following function,
• How will the graph look?

38
Lets Graph
39
• Given the following function,
• How will the graph look?

40
Lets Graph
41
• Given the following function,
• How will the graph look?

42
Lets Graph
43
Congratulations!! You just completed the
transformation of