1. 3.4: Graphs and Transformations
Worksheet Key
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2. 3.4: Graphs and Transformations
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3. 3.4: Graphs and Transformations
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3.4: Graphs and Transformations

4. 3.4: Graphs and Transformations
Quiz
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5. Parent Functions and Transformations
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3.4: Graphs and Transformations

6. What is a parent function?
A. The parent function is the simplest function with the defining characteristics of the family. Functions in the same family are transformations of their parent function.
B. There are main parent functions that are utilized through Algebra. They are the following:
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7. 3.4: Graphs and Transformations
Parent Functions
Family
Rule
Constant
f(x) = c
Linear
Quadratic
Cubic
f(x) = x
f(x) = x2
f(x) = x3
Graph
Domain
All Real Numbers
All Real Numbers
All Real Numbers
All Real Numbers
Range
All Real Numbers
All Real Numbers
y > 0
All Real Numbers
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3.4: Graphs and Transformations

8. 3.4: Graphs and Transformations
Parent Functions
Family
Rule
Squ Root
f(x) = √x
Cubic Root
f(x) = 3√x
Reciprocal
f(x) = 1/x
Squ Root
Exponential
f(x) = √x
f(x) = 2x
Abs Value
f(x) = |x|
Graph
Domain
x > 0
All Real Numbers
x ≠ 0
All Real Numbers
[0, ∞)
All Real Numbers
Range
y > 0
All Real Numbers
y ≠ 0
y > 0
y > 0
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3.4: Graphs and Transformations

9. 3.4: Graphs and Transformations
Scalar
The equation will now look like, y = a(x – h) + k
_h_ stands for the Horizontal Shift
_k_ stands for the Vertical Shift
The standard points will now be adjusted by the scalar (a)
Multiply a with the x-values of the standard points.
The scalar does not affect the new origin.
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3.4: Graphs and Transformations

10. 3.4: Graphs and Transformations
Vertical Shifts of A
For shifts of A of ax2 + bx + c = y, the bigger the A, the smaller the graph gets.
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3.4: Graphs and Transformations

11. 3.4: Graphs and Transformations
Vertical Shifts of C
For shifts of A of ax2 + bx + c = y, the change of the C, the y-intercept shifts up or down
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3.4: Graphs and Transformations

12. 3.4: Graphs and Transformations
Horizontal Shifts
For shifts of A of f(x)= a(x - h)2 + k, the change of the h, the graph shifts either left or right
If the equation is…
ADDED, it moves to the LEFT
SUBTRACTED, it moves to the RIGHT
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3.4: Graphs and Transformations

13. 3.4: Graphs and Transformations
Reflection Shifts
For horizontal shifts of f(x)= –a(x - h)2 + k or others, the change of the a, the graph shifts reflects on the axis
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3.4: Graphs and Transformations

14. Aerobic Exercises

15. Dance Moves…

16. 3.4: Graphs and Transformations
Example 1
Given the graph of f(x) = x – 3, determine the domain, range, and transformation change
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17. 3.4: Graphs and Transformations
Example 2
Given the graph of f(x) = 2x, determine the domain, range, and transformation change
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18. 3.4: Graphs and Transformations
Your Turn
Given the graph of f(x) = 1/2x + 5, determine the domain, range, and transformation change
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19. 3.4: Graphs and Transformations
Example 3
Given the graph of f(x) = 2(x + 1)2 – 3, determine the domain, range, and transformation change
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3.4: Graphs and Transformations

20. 3.4: Graphs and Transformations
Your Turn
Given the graph of y = –2(x – 3)3 + 1, determine the domain, range, and transformation change
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3.4: Graphs and Transformations

21. 3.4: Graphs and Transformations
Assignment
Worksheet
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3.4: Graphs and Transformations