1. Splash Screen

2. Five-Minute Check (over Lesson 2–6) CCSS Then/Now New Vocabulary
Key Concept: Parent Functions
Example 1: Identify a Function Given the Graph
Example 2: Describe and Graph Translations
Example 3: Describe and Graph Reflections
Example 4: Describe and Graph Dilations
Example 5: Real-World Example: Identify Transformations
Concept Summary: Transformations of Functions
Lesson Menu

3. Identify the type of function represented by the graph.
A. linear
B. piecewise-defined
C. absolute value
D. parabolic
5-Minute Check 1

4. Identify the type of function represented by the graph.
A. linear
B. piecewise-defined
C. absolute value
D. parabolic
5-Minute Check 1

5. Identify the type of function represented by the graph.
A. piecewise-defined
B. linear
C. parabolic
D. absolute value
5-Minute Check 2

6. Identify the type of function represented by the graph.
A. piecewise-defined
B. linear
C. parabolic
D. absolute value
5-Minute Check 2

7. A. $60
B. $101
C. $102
D. $148
5-Minute Check 3

8. A. $60
B. $101
C. $102
D. $148
5-Minute Check 3

9. Mathematical Practices 6 Attend to precision.
Content Standards
F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
Mathematical Practices
6 Attend to precision.
CCSS

10. You analyzed and used relations and functions.
Identify and use parent functions.
Describe transformations of functions.
Then/Now

11. family of graphs reflection line of reflection dilation parent graph
parent function
constant function
identity function
quadratic function
translation
Vocabulary

12. Concept

13. A. Identify the type of function represented by the graph.
Identify a Function Given the Graph
A. Identify the type of function represented by the graph.
Answer:
Example 1

14. A. Identify the type of function represented by the graph.
Identify a Function Given the Graph
A. Identify the type of function represented by the graph.
Answer: The graph is a V shape. So, it is an absolute value function.
Example 1

15. B. Identify the type of function represented by the graph.
Identify a Function Given the Graph
B. Identify the type of function represented by the graph.
Answer:
Example 1

16. B. Identify the type of function represented by the graph.
Identify a Function Given the Graph
B. Identify the type of function represented by the graph.
Answer: The graph is a parabola, so it is a quadratic function.
Example 1

17. A. Identify the type of function represented be the graph.
A. absolute value function
B. constant function
C. quadratic function
D. identity function
Example 1

18. A. Identify the type of function represented be the graph.
A. absolute value function
B. constant function
C. quadratic function
D. identity function
Example 1

19. B. Identify the type of function represented be the graph.
A. absolute value function
B. constant function
C. quadratic function
D. identity function
Example 1

20. B. Identify the type of function represented be the graph.
A. absolute value function
B. constant function
C. quadratic function
D. identity function
Example 1

21. Describe the translation in y = (x + 1)2. Then graph the function.
Describe and Graph Translations
Describe the translation in y = (x + 1)2. Then graph the function.
Answer:
Example 2

22. Describe the translation in y = (x + 1)2. Then graph the function.
Describe and Graph Translations
Describe the translation in y = (x + 1)2. Then graph the function.
Answer: The graph of the function y = (x + 1)2 is a translation of the graph of y = x2 left 1 unit.
Example 2

23. Describe the translation in y = |x – 4|. Then graph the function.
A. translation of the graph y = |x| up 4 units
B. translation of the graph y = |x| down 4 units
C. translation of the graph y = |x| right 4 units
D. translation of the graph y = |x| left 4 units
Example 2

24. Describe the translation in y = |x – 4|. Then graph the function.
A. translation of the graph y = |x| up 4 units
B. translation of the graph y = |x| down 4 units
C. translation of the graph y = |x| right 4 units
D. translation of the graph y = |x| left 4 units
Example 2

25. Describe the reflection in y = –|x|. Then graph the function.
Describe and Graph Reflections
Describe the reflection in y = –|x|. Then graph the function.
Answer:
Example 3

26. Describe the reflection in y = –|x|. Then graph the function.
Describe and Graph Reflections
Describe the reflection in y = –|x|. Then graph the function.
Answer: The graph of the function y = –|x| is a reflection of the graph of y = |x| across the x-axis.
Example 3

27. Describe the reflection in y = –x2. Then graph the function.
A. reflection of the graph y = x2 across the x-axis
B. reflection of the graph y = x2 across the y-axis
C. reflection of the graph y = x2 across the line x = 1.
D. reflection of the graph y = x2 across the x = –1
Example 3

28. Describe the reflection in y = –x2. Then graph the function.
A. reflection of the graph y = x2 across the x-axis
B. reflection of the graph y = x2 across the y-axis
C. reflection of the graph y = x2 across the line x = 1.
D. reflection of the graph y = x2 across the x = –1
Example 3

29. Describe the dilation on Then graph the function.
Describe and Graph Dilations
Describe the dilation on Then graph the function.
Answer:
Example 4

30. Describe the dilation on Then graph the function.
Describe and Graph Dilations
Describe the dilation on Then graph the function.
Answer: The graph of is a dilation that compresses the graph of vertically.
Example 4

31. Describe the dilation in y = |2x|. Then graph the function.
A. dilation of the graph of y = |x| compressed vertically
B. dilation of the graph of y = |x| stretched vertically
C. dilation of the graph of y = |x| translated 2 units up
D. dilation of the graph of y = |x| translated 2 units right
Example 4

32. Describe the dilation in y = |2x|. Then graph the function.
A. dilation of the graph of y = |x| compressed vertically
B. dilation of the graph of y = |x| stretched vertically
C. dilation of the graph of y = |x| translated 2 units up
D. dilation of the graph of y = |x| translated 2 units right
Example 4

33. Identify Transformations
Example 5

34. Identify Transformations
Example 5

35. Identify Transformations
Example 5

36. A. +4 translates f(x) = |x| right 4 units
Which of the following is not an accurate description of the transformations in the function ?
A. +4 translates f(x) = |x| right 4 units
B. –2 translates f(x) = |x| down 2 units
C reflects f(x) = |x| across the x-axis
D. +4 translates f(x) = |x| left 4 units
Example 5

37. A. +4 translates f(x) = |x| right 4 units
Which of the following is not an accurate description of the transformations in the function ?
A. +4 translates f(x) = |x| right 4 units
B. –2 translates f(x) = |x| down 2 units
C reflects f(x) = |x| across the x-axis
D. +4 translates f(x) = |x| left 4 units
Example 5

38. Concept

39. End of the Lesson