Unit 1 day 7 mcr 3u feb 15 2012
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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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Unit 1 day 7 mcr 3u feb 15 2012

Unit 1 Day 7

MCR 3U

Feb 15, 2012

Exploring Transformations of Parent Functions


Recall transforming

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
Vertical Translations

  • f(x) = x2

    f(x) +

y

y

0 = x2

0

1 = x2 +1

3 = x2 + 3

2 = x2+2

x


Vertical translations1
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


Horizontal translations
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


Horizontal translations1
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.


Combining translations
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


Examples
Examples

  • For f(x)=x2, graph the following:

    • f(x) + 3

    • f(x) - 1

    • f(x-2)

    • f(x+4)


Recall parent functions and their family
Recall “Parent” functions and their “Family”


Transforming non quadratics
Transforming Non-Quadratics

  • e.g. If f(x)= x , sketch f(x – 3) + 2

2

3


Translating non quadratics
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


f(x+2) -1

f(x+2)

f(x)


Conclusions for all functions
Conclusions for ALL Functions told to move it!

  • 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


Seatwork
Seatwork told to move it!

  • Page 51#1,2,4


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