1. Tuesday October 7 – Friday October 10
2.6 Families of functions
Tuesday October 7 – Friday October 10

2. Chapter 2.6 Part 1: Families of Functions
Discuss the above question with your partner. Be prepared to share how you could change the y-intercept or slope of the graph to make the line pass through point P. You have two minutes to think about and discuss this.

3. Explore Translations
Describe the relationship between the two graphs. Then, with the equations of the functions graphed, comment on how the equations differ. Is there a connection between the way the equation differs and the way the graphs are related?
You may raise your hand or talk to your neighbor if you have a question.

4. Time for Notes!
A parent function is the simplest form in a set of functions that form a family.
Example: The linear functions are a family of functions, and it’s parent function, of simplest form, is y=x.
Every linear function is a transformation of y=x
Every function within a family is a transformation of the parent function.

5. One type of Transformation
A translation shifts the graph of the parent function up, down, or both without changing shape or orientation.
For a positive constant k, and a parent function f(x), f(x)±𝑘 is a vertical translation.
For a positive constant h, and a parent function f(x), f(x±ℎ) is a horizontal translation.

6. Let’s Try it! Now, graph the line y=x.
Graph and write the equation of the line y=x shifted 3 units to the right.
Using this new equation, graph and write the equation of the line shifted down 2 units.

7. Engage: Graph the following function on your own graph paper.
In one color, translate the graph up two units and write the equation of the parabola.
Then in another color, have the students transfer the original parabola to the left 4 units and write the equation of the parabola.
How would we reflect this graph across the x-axis or y-axis? Discuss with your partner how you think you could flip the graph across either axis.

8. Explore Reflections
For each of the following graphs, draw the reflection across the indicated axis. Then complete a table of values for both the original function and the reflection.
You may raise your hand or talk to your neighbor if you have a question.

9. How did we do? (Problem 1) What do you notice about the y-values?X Y X Y
What do you notice about the y-values?
Reflect across the x-axis

10. How did we do? (Problem 2) What do you notice about the x-values?X Y
What do you notice about the x-values?
Reflect across the y-axis

11. Time for Notes!
A reflection flips the graph of a function across a line, such as the x- or y-axis.
When you reflect a graph in the y-axis, the x-values change sign and the y-values stay the same. For a function f(x), the reflection in the y-axis is f(-x).
When you reflect a graph in the x-axis, the x-values stay the same and the y-values change sign. For a function f(x), the reflection in the x-axis is –f(x).

12. Last Activity and Reminders!
Look Back:
Take an index card and fold it in half to create two columns. Label the columns, “What I learned” and “How I learned it”. Take a few moments to write down information from today’s lesson that you learned and recall how you learned it. Put your name on the back and turn it in on the way out of class. This will count towards your grade.
Homework Assignment:
2.6 Practice (pg.55) 
2.6 homework: pg. 113 #8-21

13. Engage
Look at the graph of the following function. With your table partner, collaborate to discover the function of the line using the information about translations and reflections of functions from last class.

14. Explore Vertical Stretch and Compression
Consider the graph of two functions, represented by a solid line and dotted line. Complete the tables for each graph, identifying the x-value, y-values of the solid line, y-values of the dotted line, and what you notice between the y-values from the solid line to the dotted line.

15. How did we do? (Problem 1) X
Y (solid)
Y (dotted)
Relationship?
What is happening to the solid-lined graph to get to the dotted-lined graph?

16. How did we do? (Problem 2) X
Y (solid)
Y (dotted)
Relationship?
What is happening to the solid-lined graph to get to the dotted-lined graph?

17. Time for Notes!
A vertical stretch multiplies all y-values of a function by the same factor greater than 1.
A vertical compression reduces all y-values of a function by the same factor between 0 and 1.
For a function f(x) and a constant a, y=af(x) is a vertical stretch when a>1 and a vertical compression when 0<a<1.

18. Look Back Continued…
Students will take out their index card from earlier in the activity and continue writing in the columns, what they’ve learned and how they’ve learned in. Take a few moments to write down information from the lesson on any transformations that you learned and recall how you learned it. Work on this by yourself.

19. Engage!
I will name a type of transformation we have learned this week.
I will play a song and you will have the duration of me playing the song to think and/ or discuss with their partners as many details as you can about that transformation.
You will be standing while the song is playing.
When I stop the song, the last student to sit down will be the student to tell us about that transformation.

20. Summary

21. Example:
y= 2(x+2)2-3

22. Example:
y= -|x-1|+5

23. You Do
y= (-x-3) b) y=2|x+4|-1

24. Last Activity and Reminders
Think-Pair-Share
Take two minutes to look at the index card from our Look Back activity. If there is anything you want to add to it today from the types of problems involving multiple transformations, please write them down. Then, with your partner, compare your index cards and see if there was anything you wrote down that your partner did not. Is there anything your partner wrote that seems important that you may have missed on your own card?
Be prepared to share some of your discussion topics!
Homework Assignment:
2.6 Practice (pg.55 and 56) 
2.6 homework: pg. 113 #8-21
2.6 homework: pg. 118 #8-20