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Parent Functions & Transformations

Parent Functions & Transformations. Objective: identify common types of functions; describe transformations given an equation. How does adding/subtracting/multiplying affect the shape or position of a graph?. Linear. f (x)=x. f (x)= a (x – h )+ k. Quadratic. f (x)=x 2.

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Parent Functions & Transformations

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  1. Parent Functions & Transformations Objective: identify common types of functions; describe transformations given an equation. How does adding/subtracting/multiplying affect the shape or position of a graph?

  2. Linear f(x)=x f(x)=a(x – h)+k

  3. Quadratic f(x)=x2 f(x)=a(x – h)2+k

  4. Cubic f(x)=x3 f(x)=a(x – h)3+k

  5. Absolute Value f(x)=|x| f(x)=a|x – h|+ k

  6. Square Root f(x)=√x

  7. Exponential f(x)= ex f(x)= ab(x – h) + k

  8. Logarithm f(x)= log(x) f(x)= alog(x – h) + k

  9. Reciprocal

  10. What is the parent function?

  11. What is the parent function?

  12. What is the parent function?

  13. What is the parent function?

  14. What is the parent function?

  15. What is the parent function?

  16. What is the parent function?

  17. What is the parent function?

  18. What is the parent function?

  19. What is the parent function?

  20. Transformation • A change in the size/shape of the graph • TRANSLATION = Move (slide) • REFLECTION = Flip • STRETCH • COMPRESSION

  21. OUTISDE Transformations • Affect the Y values • Change the graph VERTICALLY • (INSIDE) Transformations • Affect the X values • Change the graph HORIZONTALLY • ACT “OPPOSITE”

  22. Reflects over x-axis y = -a(x–h) +k Vertical stretch or compression Move up/down Move right/left

  23. Ex 1.)f(x) = (x + 5)2 Parent: Inside/outside?: Transformation:

  24. Ex 2.) Parent: Inside/outside?: Transformation:

  25. Ex 3.) Parent: Inside/outside?: Transformation:

  26. Ex 4) f(x) = 3(x – 5)2 + 1 Parent: Transformations:

  27. Ex 5) Parent: Transformations:

  28. Ex 6) Parent: Transformations:

  29. Sketch New Graph Parent: y = x2 y = x2 – 3

  30. Sketch New Graph Parent: y = x2 y = (x – 3)2

  31. Sketch New Graph Parent: y = x2 y = 2x2

  32. Sketch New Graph Parent: y = x2 y = -2(x + 6)2 + 1

  33. Sketch New Graph Parent: y = x2 y = 3x2 – 4

  34. Sketch New Graph Parent: y = √x

  35. Sketch New Graph Parent: y = √x

  36. Sketch New Graph Parent: f(x) = |x|

  37. Sketch New Graph Parent: f(x) = |x|

  38. Write the equation of an absolute value graph that has been translated 2 units to the right y = |x – 2|

  39. Write the equation of an absolute value graph that has been moved 4 units down y = |x| – 4

  40. Write the equation of an absolute value graph that has been stretched by 2 and moved up 7 y = 2|x| + 7

  41. Write the equation of an absolute value graph that has been flipped over the x-axis and moved to the left 1 y = -|x+1|

  42. Write the equation of an absolute value graph that has been translated 5 units to the left and 2 units down y = |x + 5| - 2

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