Transformations of H & K
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Transcript of Transformations of H & K
Transformations of H & K
Unit 2: Properties and Attributes of Functions
Any function can be transformed!
RULES
Vertical Translation, Shifts UP by adding K
Horizontal Translation, Slides right by subtracting h
K just adds to the function valueH lies by changing the location of X
y= 𝑓 (𝑥 )+𝑘
x
y
-5 1
-2 4
0 3
2 2
3 0
4 2
6 0
7 -1
-5 5
-2 9
0 7
2 6
3 4
4 6
6 4
7 3
NEW GRAPH
Domain doesn’t change!
x
y
y= 𝑓 (𝑥 )−𝑘-5 1
-2 4
0 3
2 2
3 0
4 2
6 0
7 -1
-5 -4
-2 -1
0 -2
2 -3
3 -5
4 -3
6 -1
7 -2
NEW GRAPH
Domain doesn’t change!
x
y
-5 1
-2 4
0 3
2 2
3 0
4 2
6 0
7 -1
-4 1
-1 4
1 3
3 2
4 0
5 2
7 0
8 -1
NEW GRAPH
Range doesn’t change!
y= 𝑓 (𝑥−h )
x
y
-5 1
-2 4
0 3
2 2
3 0
4 2
6 0
7 -1
-7 1
-4 4
-2 3
0 2
1 0
2 2
4 0
5 -1
NEW GRAPH
Range doesn’t change!
y= 𝑓 (𝑥+h )
is translated 5 units right and 2 units down.
is translated 4 units to the left and 1 unit up.
From only a description
𝑦= 𝑓 (𝑥−5 )−2
𝑦= 𝑓 (𝑥+4 )+1