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Warm UP! Name each parent graph…

Warm UP! Name each parent graph…. absolute value. quadratic. linear. square root. cubic. rational. Transformations. Transformations. What happens when something transforms? Transformation - a movement or change of a function. There are three types Stretch/Shrink

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Warm UP! Name each parent graph…

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  1. Warm UP!Name each parent graph… absolute value quadratic linear square root cubic rational

  2. Transformations

  3. Transformations What happens when something transforms? Transformation- a movement or change of a function. • There are three types • Stretch/Shrink • Horizontal/Vertical Shift • Reflections

  4. When we talk about “transformations” we are talking about where the VERTEX is moving! What point does each graph have in common?

  5. Given the following function, If: k > 0, then shift the graph “k” units up If: k < 0, then shift the graph “k” units down Vertical Shifts

  6. Given the following function, Since k > 0, then shift the graph “3” units up

  7. How will the graph look?

  8. How will the graph look?

  9. How will the graph look?

  10. Given the following function, We get the expression (x - h) and equal it to zero x - h = 0 x = h If: h> 0, then shift the graph “h” units to the rightIf: h< 0, then shift the graph “h” units to the left Horizontal Shifts

  11. Given the following function, x – 1 = 0 x = 1 Since 1> 0, then shift the graph “1” unit right

  12. How will the graph look?

  13. How will the graph look?

  14. How will the graph look?

  15. Combining vertical & horizontal shifts Example of function that is shifted down 4 units and right 6 units from the original function.

  16. Describe the Transformations

  17. How will the graph look?

  18. How will the graph look?

  19. How will the graph look?

  20. Stretch/Shrink Given the following function, For this equation, a determines how fat or skinny the graph will be. if: |a|>1, then the graph is stretched closer to the y-axis if: |a|=1, then the graph remains the same if: 0<|a|<1, then the graph is shrunk (further from the y-axis)

  21. Reflections • The graph of f(x) is the reflection of the graph of f(x) across the x-axis. • The graph of f(x) is the reflection of the graph of f(x) across the y-axis. How do the following graphs reflect?

  22. Given the following function, Since |5| > 0, then the graph is closer to the y-axis

  23. How will the graph look?

  24. How will the graph look?

  25. How will the graph look?

  26. How will the graph look?

  27. Given the following function, Since 4 > 0, shift the graph “4” units up x – 1 = 0 x = 1 Since 1> 0, then shift the graph “1” unit to the right Since |5| > 0 shift the graph closer to the y-axis.

  28. Let’s Graph

  29. How will the graph look?

  30. How will the graph look?

  31. How will the graph look?

  32. How will the graph look?

  33. How will the graph look?

  34. How will the graph look?

  35. How will the graph look?

  36. Congratulations!!You just completed the transformation of ALL FUNCTIONS ARE TRANSFORMED WITH THE SAME PROPERTIES

  37. Name all the transformations:

  38. Write the Equation to this Graph

  39. Write the Equation to this Graph

  40. Write the equation... 3) …of the quadratic equation that has been shifted down 6 units. y = x2 - 6 4) …of the square root function that has been shifted right 25 units and up 2004 units.

  41. Homework • Page 53 # 1 - 15 all • Do NOT graph. • Write what would happen to each graph • Ex: up 1 unit, right 2 units

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