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Transformations of Functions

- Viviana C. Castellón
- East Los Angeles College
- MEnTe
- Mathematics Enrichment
- through Technology

Graphing

- Given the following function,
- If a gt 0, then shift the graph a units up
- If alt0, then shift the graph a units down

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

Lets Graph

- Given the following function,
- How will the graph look?

Lets Graph

- Given the following function,
- Since a lt 0, then the graph will be
- shift down 3 units

Lets Graph

- Given the following function,
- How will the graph look?

Lets Graph

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

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

Lets Graph

- Given the following function,
- How will the graph look?

Lets Graph

- Given the following function,
- How will the graph look?

Lets Graph

- Given the following function,
- How will the graph look?

Lets Graph

- 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

- Given the following function,
- How will the graph look?

Lets Graph

- Given the following function,
- How will the graph look?

Lets Graph

- Given the following function,
- How will the graph look?

Lets Graph

- Given the following function,
- How will the graph look?

Lets Graph

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

Lets Graph

Lets Graph

Lets Graph

- 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

- Given the following function,
- How will the graph look?

Lets Graph

- Given the following function,
- How will the graph look?

Lets Graph

- Given the following function,
- How will the graph look?

Lets Graph

- Given the following function,
- How will the graph look?

Lets Graph

Congratulations!! You just completed the

transformation of