Unit 1 Day 7MCR 3UFeb 15, 2012

cdxaxf 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

0 = x23 = x2 + 3

f(x) = x2

f(x) + 01 = x2 +12 = x2+2

x

yy

f(x) = x2

f(x) + 0 = x2-1 = x2 -1-2 =x2 - 20-3 = x2

-3

x

yy

Adding c to f(x) moves the graph up by c units if c is positive, down if c is negative

f(x) = x2

f(x + 0) = (x+0)2f(x+1)=(x+1)2f(x+2) =(x+2)2 f(x+3) = (x+3)2

x

yy

f(x) = x2

f(x – 0) = (x-0)2f(x-1)=(x-1)2f(x-2) =(x-2)2 f(x-3) = (x-3)2

x

yy

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:

f(x) = x2f(x-2)=(x-2)2f(x-2) +3 =(x-2)2 +3

x

yy

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

Parent Graph Family Effects

2)( xxf

xxf )( bmxxf )(

cdxaxf 2)()(

xxf )( cdxaxf )()(

xxf

1)( c

dx

axf

)(

xxf )( cdxaxf )(

m slope

b inty

a verticalncompressiostrech /

c ntranslatiodownup /

d ntranslatiorightleft /

e.g. If f(x)= x , sketch f(x – 3) + 2

xxf )(

3)3( xxf 232)3( xxf

3

2

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

2

1)2(

x

xfx

xf1

)( 12

11)2(

x

xf-2

1

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) -1f(x+2)f(x)

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.

cdxafxg )()(

“f” represents any parent function

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