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Exploring Transformations of Parent Functions

Unit 1 Day 7 MCR 3U Feb 15, 2012. Exploring Transformations of Parent Functions. a = adjusting shape (compress, stretch or reflect) c = moving up/down d = moving left/right Note: a ,c ,d  R Remember f(x) means – function with variable x. Recall “Transforming”. Vertical Translations.

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Exploring Transformations of Parent Functions

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  1. Unit 1 Day 7 MCR 3U Feb 15, 2012 Exploring Transformations of Parent Functions

  2. a = adjusting shape (compress, stretch or reflect) c = moving up/down d = moving left/right Note: a ,c ,d  R Remember f(x) means – function with variable x Recall “Transforming”

  3. Vertical Translations • f(x) = x2 f(x) + y y 0 = x2 0 1 = x2 +1 3 = x2 + 3 2 = x2+2 x

  4. Vertical Translations • f(x) = x2 f(x) + y y 0 = x2 -1 = x2 -1 0 -3 = x2-3 -2 =x2 - 2 x Adding c to f(x) moves the graph up by c units if c is positive, down if c is negative

  5. Horizontal Translations • f(x) = x2 y y f(x + 0) = (x+0)2 f(x+1)=(x+1)2 f(x+2) =(x+2)2 f(x+3) = (x+3)2 x

  6. Horizontal Translations • f(x) = x2 y y f(x – 0) = (x-0)2 f(x-1)=(x-1)2 f(x-2) =(x-2)2 f(x-3) = (x-3)2 x • Changing a function from f(x) to f(x-d) will move the graph d units to the right. • Changing a function from f(x) to f(x+d) will move the graph d units to the left.

  7. Combining Translations • If f(x) = x2, graph f(x-2) +3: y y f(x) = x2 f(x-2)=(x-2)2 f(x-2) +3 =(x-2)2 +3 x

  8. Examples • For f(x)=x2, graph the following: • f(x) + 3 • f(x) - 1 • f(x-2) • f(x+4)

  9. Recall “Parent” functions and their “Family”

  10. Transforming Non-Quadratics • e.g. If f(x)= x , sketch f(x – 3) + 2 2 3

  11. Translating Non-Quadratics • So, for any function, if you can graph f(x), you can shift it to graph new functions! • E.g. if f(x) = 1/x, sketch f(x+2)+1 1 -2

  12. You can even be given a graph of something weird, and be told to move it! • e.g. Given f(x) below, sketch f(x+2) -1 f(x+2) -1 f(x+2) f(x)

  13. Conclusions for ALL Functions • The constants c, and d each change the location of the graph of f(x). • The shape of the graph of g(x) depends on the graph of the parent function g(x) and on the value of a. “f” represents any parent function

  14. Seatwork • Page 51#1,2,4

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