Exploring Transformations of Parent Functions

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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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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
• f(x) = x2

f(x) +

y

y

0 = x2

0

1 = x2 +1

3 = x2 + 3

2 = x2+2

x

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

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)

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

Seatwork
• Page 51#1,2,4