1. 1.7 Notes: Transformations of Functions
Date:
1.7 Notes: Transformations of Functions
Lesson Objective: Use rigid and nonrigid transformations to graph functions
You will need: graph paper
Real-World App: How does the graph of fuel used by trucks differ from the parent graph?
This is Jeopardy!!!: These are the rigid transformations of graphs and what happens algebraically during the transformation.

2. Lesson 1: Rigid Transformations
Translation:

3. Lesson 1: Rigid Transformations
Translation: Vertical and/or horizontal shift
1. Vertical shift +c: h(x) = f(x) + c
2. Horizontal shift +c: h(x) = f(x + c)

4. Lesson 1: Rigid Transformations
Translation: Vertical and/or horizontal shift
1. Vertical shift +c: h(x) = f(x) + c
2. Horizontal shift +c: h(x) = f(x + c)

5. Lesson 1: Rigid Transformations
Reflection: The mirror image across an axis.
1. x-axis: h(x) = -f(x)
2. y-axis: h(x) = f(-x)

6. Lesson 1: Rigid Transformations
Reflection: The mirror image across an axis.
1. x-axis: h(x) = -f(x)
2. y-axis: h(x) = f(-x)

7. Lesson 2: Finding Equations from Graphs
Identify the parent graph and the transforma-tion shown. Write an equation for each function. A.

8. Lesson 2: Finding Equations from Graphs
Identify the parent graph and the transforma-tion shown. Write an equation for each function. B.

9. Lesson 2: Finding Equations from Graphs
Identify the parent graph and the transforma-tion shown. Write an equation for each function. C.

10. Lesson 2: Finding Equations from Graphs
Identify the parent graph and the transforma-tion shown. Write an equation for each function. D.

11. Lesson 3: Graphing Transformations
Identify the parent function, f. Describe the sequence of transformations from f to g. Sketch the graph of g. Use function notation to write g in terms of f.
A. g(x) = (x + 3)³ – 4

12. Lesson 3: Graphing Transformations
Identify the parent function, f. Describe the sequence of transformations from f to g. Sketch the graph of g. Use function notation to write g in terms of f.
B. g(x) = -(x + 10)² + 5

13. Lesson 3: Graphing Transformations
Identify the parent function, f. Describe the sequence of transformations from f to g. Sketch the graph of g. Use function notation to write g in terms of f.
C. g(x) = 6 – |x – 5|

14. Lesson 3: Graphing Transformations
Identify the parent function, f. Describe the sequence of transformations from f to g. Sketch the graph of g. Use function notation to write g in terms of f.
D. g(x) = 𝑥

15. Lesson 3: Graphing Transformations
Identify the parent function, f. Describe the sequence of transformations from f to g. Sketch the graph of g. Use function notation to write g in terms of f.
E. g(x) = 2[[x + 5]]

16. Lesson 4: Nonrigid Transformations
Nonrigid Transformations: Vertical or horizontal stretch or shrink
Vertical: g(x) = cf(x)
Stretch: c > 1
Shrink: 0 < c < 1
Horizontal: g(x) = f(cx)
Stretch: 0 < c < 1
Shrink: c > 1

17. Lesson 4: Nonrigid Transformations
Compare the graph of each function with the graph of f(x) = x³ – 5x.
g(x) = 2f(x)
h(x) = 1 2 f(x)

18. Lesson 4: Nonrigid Transformations
Compare the graph of each function with the graph of f(x) = x³ – 5x.
j(x) = f(2x)
k(x) = f(½x)

19. 1.7: DIGI Yes or No
Use the graph of f(x) = x³ to sketch the graph of h(x) = (x + 2)³ + 1.
The graph of f(x) = x4 is shown to the left. Find the equation of the function of the graph to the right.
Continued on next slide

20. 1.7: DIGI Yes or No
Compare the graph of h(x) = 3|x| to f(x) = |x|.
Compare the graph of g(x) = f(2x) to f(x) = 2 - x³.