Exploring Transformations of Parent Functions
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Transcript of Exploring Transformations of Parent Functions
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
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
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.
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 /
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