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Warm Up

Warm Up. What is the domain, range, max/min, interval of increase and decrease for the following graph (list critical points first). Parent Function Transformation. Lesson Essential Question – How do we move graphs?. f(x) = x. f (x) = x ². f(x) = x ³. f(x) = √x. f(x) = lxl. f(x) = 1/x.

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Warm Up

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  1. Warm Up • What is the domain, range, max/min, interval of increase and decrease for the following graph (list critical points first)

  2. Parent Function Transformation Lesson Essential Question – How do we move graphs?

  3. f(x) = x

  4. f(x) = x²

  5. f(x) = x³

  6. f(x) = √x

  7. f(x) = lxl

  8. f(x) = 1/x

  9. Putting a NEGATIVE in front • What happens when we put a negative in front of the function? • There is a reflection

  10. Y = - x • See how it flipped?  because of the –x • Does it flip over the x or y axis?

  11. Y = -lxl • Reflection over x or y?

  12. Y = -x³ Reflection over x or y?

  13. Y = -x² • Reflection over x or y?

  14. Adding a “+” to it • Adding a “+” shifts that whole function (from the critical point) UP the y axis that many points. • If it is +3, then the graph shifts up 3

  15. Y = x + 6 • Start at the origin (0,0) and move up 6

  16. Y = lxl + 2 • Always start at the origin

  17. Y = √x + 3

  18. What happens if we have a NEGATIVE? • Then the entire graph moves DOWN the y axis that many points • If you have a “- 4”, then you move down the y axis 4 points from the origin.

  19. Y = x² - 4

  20. Y = x³ - 3

  21. Y = √x – 4

  22. Let’s Review • A negative IN FRONT of the x means it is a reflection • Is this a reflection over the X or Y axis?

  23. Let’s Review • A “+” AFTER the x means you move it up the y axis • Always start at the origin then move

  24. Let’s Review • A “-” after the x means you move it down the y axis

  25. Let’s Confuse • Sometimes you will have to do 2 things • Like a reflection AND move it up the y axis • You need to pay attention to the equation to figure out what to do

  26. Y = - lxl + 2

  27. Y = -x + 1

  28. Y = -x² + 1

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