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# Exploring Transformations of Parent Functions - PowerPoint PPT Presentation

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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MCR 3U

Feb 15, 2012

### Exploring Transformations of Parent Functions

c = moving up/down

d = moving left/right

Note: a ,c ,d  R

Remember f(x) means – function with variable x

Recall “Transforming”

• f(x) = x2

f(x) +

y

y

0 = x2

0

1 = x2 +1

3 = x2 + 3

2 = x2+2

x

• 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

• 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

• 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.

• 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

• 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”

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

2

3

• 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 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 told to move it!

• Page 51#1,2,4