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Graph Transformations Exploration: Equations and Creative Interpretations

Explore graph transformations including reflections, shifts, and stretches. Identify parent functions and transformations of equations. Create dance interpretations for equations. Understand even and odd functions graphically and algebraically. Analyze end behavior based on degree and leading coefficient. Practice identifying transformations and behaviors in graphs and equations.

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Graph Transformations Exploration: Equations and Creative Interpretations

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  1. Warm UP 3/28/09 Describe the transformations of each graph: UP 3 REFLECT OVER X AXIS RIGHT 4 LEFT 2 DOWN 7

  2. Practice Identify the parent function and the transformations for each equation: 1. 2. 3. 4.

  3. It is also possible to look at a graph and determine the equation using the TRANSFORMATIONS! • What parent function is the graph related to? • Is the VERTEX moved up or down? • Is the VERTEX moved left or right? • Is the graph reflected over the x or y axis? • Is the graph stretched or shrunken?

  4. Write the Equation to this Graph

  5. Write the Equation to this Graph

  6. Write the Equation to this Graph

  7. Write the Equation to this Graph

  8. Write the Equation to this Graph

  9. Write the Equation to this Graph

  10. Write the Equation to this Graph

  11. Write the Equation to this Graph

  12. Write the Equation to this Graph

  13. Degree and Term Naming Review

  14. Creative Time Create a dance for each equation below so that if you were to dance this equation, someone could guess which one you’re talking about.

  15. Even and Odd Functions (algebraically) A function is even if f(-x) = f(x) If you plug in -x and get the original function, then it’s even. A function is odd if f(-x) = -f(x) If you plug in -x and get the opposite function, then it’s odd.

  16. Even, Odd or Neither? Ex. 1 Graphically Algebraically EVEN

  17. Even, Odd or Neither? Ex. 2 Graphically Algebraically ODD

  18. Ex. 3 Even, Odd or Neither? Graphically Algebraically EVEN

  19. Ex. 4 Even, Odd or Neither? Graphically Algebraically Neither

  20. Your turn! Even, Odd or Neither? EVEN ODD

  21. What do you notice about the graphs of even functions? Even functions are symmetric about the y-axis

  22. What do you notice about the graphs of odd functions? Odd functions are symmetric about the origin

  23. EVEN

  24. ODD

  25. Neither

  26. Neither

  27. EVEN

  28. ODD

  29. Neither

  30. EVEN

  31. End Behavior degree • If the __________ is even and the leading coefficient is _________, then • the left side of your graph goes _______ and the right side of your graph goes __________. positive up up degree • If the __________ is even and the leading coefficient is _________, then • the left side of your graph goes _______ and the right side of your graph goes __________. negative down down

  32. End Behavior degree • If the __________ is odd and the leading coefficient is _________, then • the left side of your graph goes _______ and the right side of your graph goes __________. positive down up degree • If the __________ is odd and the leading coefficient is _________, then • the left side of your graph goes _______ and the right side of your graph goes __________. negative up down

  33. Describe the end behavior!

  34. Homework Pg 128 # 1 – 3 and # 10 - 16

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