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Transformations
We are going to look at some transformation rules today:
xfxf it to change and function a takeLets
this?do hen wefunction w theofgraph the tohappensWhat
xxf :Ex
xxf
Lets check the graphs of each function to see what happens!
xxf xxg
When you negate the x, you are reflecting the graph in the y-axis!
xfxf it to change and function a takeLets
this?do hen wefunction w theofgraph the tohappensWhat
2 :Ex xxf This means we are negating the function, not x. So we just put a negative in front of the function.
2xxf
2 xxg
When you negate the function, or y, you are reflecting the graph in the x-axis!
Page 15
When you negate the x, you are reflecting the graph in the y-axis!
xxf xxg
Page 15
xxf
When you negate the function, or y, you are reflecting the graph in the x-axis!
xxg
Page 165
Since the x is negated, then we would reflect the function over the y-axis. Since there is a negative in front of the function, then we reflect it over the x-axis. This is also the same as a reflection through the origin!
Page 16
When we reflect over the x-axis, we negate the function, or y.
The function is negated, or y, so we reflect over the x-axis.
Homework
•TEQ
axfxf it to change and function a takeLets
this?do hen wefunction w theofgraph the tohappensWhat
)sin( :Ex xxf
xxf 2sin2
Lets check the graphs of each function to see what happens!
When you multiply the x by a, it is a horizontal dilation of 1/a.
xxf sin xxg 2sin
aHD 1
,
2
1,H
D
x
afxf
1 it to change and function a takeLets
this?do hen wefunction w theofgraph the tohappensWhat
)sin( :Ex xxf
xxf2
1sin
2
1Lets check the graphs of each function to see what happens!
When you multiply the x by 1/a, it is a horizontal dilation of a.
xxf sin
xxg
2
1sin
aHD ,
2,HD
xfxf a it to change and function a takeLets
this?do hen wefunction w theofgraph the tohappensWhat
)sin( :Ex xxf When you multiply the function by a, just put a in front of the function.
When you multiply f(x) by a, it is a vertical dilation of a.
xxf sin
aVD ,
xxg sin22,VD
xfxfa
1 it to change and function a takeLets
this?do hen wefunction w theofgraph the tohappensWhat
)sin( :Ex xxf When you multiply the function by 1/a, just put 1/a in front of the function.
When you multiply f(x) by 1/a, it is a vertical dilation of 1/a.
xxf sin
aVD 1
,
xxg sin2
1
2
1,V
D
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2. ofdilation horizontal a is This
2,HD
Page 18
5. ofdilation verticala is This
5,VD
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The y-intercept of the original function is -6. When you do a vertical dilation, you multiply the y-value.
6,0 12,0
I multiplied the y-value by 2, and got the new y-intercept.
Page 18
We are multiplying the x-value by 2, which is a horizontal dilation of ½. So we multiply all of the x-values by ½.
We are multiplying the function by 2, which is a vertical dilation of 2. So we multiply all of the y-values by 2.
Homework
•Page 24
#3,6,7,9,10
