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Understanding Linear and Exponential Transformations in Graphing

This lesson focuses on linear and exponential transformations, including shifts, compressions, and stretches. Students will engage in various activities to explore how transformations affect the coordinates of points on a graph. By shifting points on the graph using colored M&Ms, students will visualize and understand how these transformations influence the ordered pairs, slopes, and y-intercepts of linear equations. Important dates for quizzes and tests are also provided to help students prepare for their assessments.

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Understanding Linear and Exponential Transformations in Graphing

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  1. Tuesday, November 12th Warm-Up F(x)=4x + 8 G(x)=2x²-4 Find (f-g)(x) Find (g•f)(x) September 27th

  2. Species Project WAY TO GO!!!!!!

  3. Unit 5 Transformations • Linear transformations-shifts, compressions, and Stretches • Exponential Transformation-Shifts, compressions, and stretches • Characteristics of graphs-domain, range, end behavior, asymptotes, x and y intercepts, Increasing and Decreasing, local max and local min

  4. Important Dates Tuesday, November 19th-Quiz on Linear Transformations Friday, December 6th-TEST #6 LAST TEST OF THE SEMESTER

  5. Graphing Transformations

  6. Part 1: Translating Points

  7. Discovery Activity Step 1 • Draw a x and y axis on your graph paper • Separate your M & M’s into colored groups

  8. Discovery Activity Step 2 • Place an orange M & M on (-4, 5) Shift the M & M up 4 units. And put a different orange M and M/ What is the new point?

  9. Discovery Activity Step 3 • Place a red M & M on (3, 4) Shift the M & M down 5 units. Place a different red m and m at this point What is the new point?

  10. Discovery Activity Step 4 • Place a green M & M on (1, -3) Shift the M & M up 2 units. Place a new green M and M at the new point. What is the new point?

  11. Discussion Question #1 When you shift the M & M up or down, what changes in your ordered pair??!

  12. Discovery Activity Step 1 • Place a green M & M on (-2, 5) Shift the M & M left 4 units. What is the new point?

  13. Discovery Activity Step 2 • Place a gred M & M on (3, -3) Shift the M & M left 3 units. What is the new point?

  14. Discovery Activity Step 3 • Place an organe M & M on (1,5) Shift the M & M right 4 units. What is the new point?

  15. Discussion Question #2 When you shift the M & M right or left, what changes?!

  16. Part 2: Translating Equations

  17. Y = x Step 1: Fill in the table Step 2: Graph with green

  18. Step 3: Shift graph up 4 units-red

  19. Step 4: Shift graph Down 4 units-brown

  20. Discussion Questions • Did the slope change between your three graphs? • Did the y-intercept change between your three graphs? • Did you x’s or y’s change when you made a shift up or down • How would you write the following new equations g(x) compared to f(x) in green F(x)=x • Shift up 4 units • Shift down 4 units

  21. Y = x Step 1: Shift graph Left 4 units

  22. Step 2: Shift graph right 4 units

  23. Discussion Questions • Did the slope change between your three graphs? • Did the y-intercept change between your three graphs? • Did you x’s or y’s change when you made a shift up or down • How would you write the following new equations g(x) compared to f(x) in green F(x)=x • Shift up 4 units • Shift down 4 units

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