trig - 11/27/2015 lo: nonrigid transformations compare the graphs of the three functions. describe...
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Trig - 04/18/23 LO: Nonrigid Transformations
Compare the graphs of the three functions. Describe the transformation from f(x) to g(x) and h(x)?
#110 HW: p49 33-45 all, 51-63 odds Honors: 49, 50
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f x( ) = x 3
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g x( ) = x − 4( )3
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h x( ) = − x +2( )3 +8
4 units to the right
2 units to the leftReflected on the x-axis8 units up
A. Shift leftB. Shift rightC. Shift upD. Shift downE. Reflected on x-axisF. Reflected on y-axis
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f x( ) = x 2 −9
A. Shift left
B. Shift right
C. Shift up
D. Shift down
E. Reflected on x-axis
F. Reflected on y-axis
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f x( ) = x −9
A. Shift leftB. Shift rightC. Shift upD. Shift downE. Reflected on x-axisF. Reflected on y-axis
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f x( ) = − x
A. Shift left
B. Shift right
C. Shift up
D. Shift down
E. Reflected on x-axis
F. Reflected on y-axis
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f x( ) = x + 3
A. Shift left
B. Shift right
C. Shift up
D. Shift down
E. Reflected on x-axis
F. Reflected on y-axis
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f x( ) = x − 4
Nonrigid Transformations
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f x( ) = ax 2
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f x( ) = ax( )2
vertical horizontal
> 1 narrower
< 1 wider
stretch
stretch
shrink
shrink
Nonrigid TransformationsFor the function the transformation stretches
vertically if |a| > 1.€
f x( ) = x 2
( ) 2axxh =
vertical stretch(looks narrower)
Nonrigid TransformationsFor the function the transformation shrinks
horizontally if |a| > 1.€
f x( ) = x 2
( ) ( )2axxh =
horizontal shrink(looks narrower)
Nonrigid TransformationsFor the function the transformation shrinks
vertically, if |a| < 1.€
f x( ) = x 2
( ) 2axxh =
vertical shrink(looks wider)
Nonrigid TransformationsFor the function the transformation stretches
horizontally, if |a| < 1.€
f x( ) = x 2
( ) ( )2axxh =
horizontal stretch(looks wider)
Nonrigid TransformationsFor the function ( )bxafy =
|a| > 1 or |b| > 1 looks narrower.|a| > 1 vertical stretch|b| > 1 horizontal shrink
|a| < 1 or |b| < 1 looks wider.|a| < 1 vertical shrink|b| < 1 horizontal stretch
( ) 22xxf =
( ) ( )22xxf =
( ) 2
2
1xxf =
( )2
2
1⎟⎠⎞
⎜⎝⎛= xxf
outside
inside
Nonrigid TransformationsFor the functionthe transformation is a
( ) xxf =
(a) Vertical stretch(b) Vertical shrink(c) Horizontal stretch(d) Horizontal shrink
( ) xxh 3=
|a| > 1outside
Nonrigid TransformationsFor the functionthe transformation is a
( ) xxf =
(a) Vertical stretch(b) Vertical shrink(c) Horizontal stretch(d) Horizontal shrink
( ) xxh4
1=
|b| < 1inside
Nonrigid TransformationsFor the functionthe transformation is a
( ) 3xxf =
(a) Vertical stretch(b) Vertical shrink(c) Horizontal stretch(d) Horizontal shrink
( ) ( )36xxh =
|b| > 1
inside
TransformationsCompare the graph of the function with the graph of ( ) xxf =
( ) 3−= xxh
(a) Vertical stretch(b) Vertical shrink(c) Horizontal shrink(d) Horizontal stretch(e) Horizontal shift to the right(f) Horizontal shift to the left(g) Vertical shift to the down(h) Vertical shift to the up(i) Reflection on the x-axis(j) Reflection on the y-axis
TransformationsCompare the graph of the function with the graph of ( ) xxf =
(a) Vertical stretch(b) Vertical shrink(c) Horizontal shrink(d) Horizontal stretch(e) Horizontal shift to the right(f) Horizontal shift to the left(g) Vertical shift to the down(h) Vertical shift to the up(i) Reflection on the x-axis(j) Reflection on the y-axis
( ) xxh 3=
TransformationsCompare the graph of the function with the graph of ( ) xxf =
(a) Vertical stretch(b) Vertical shrink(c) Horizontal shrink(d) Horizontal stretch(e) Horizontal shift to the right(f) Horizontal shift to the left(g) Vertical shift to the down(h) Vertical shift to the up(i) Reflection on the x-axis(j) Reflection on the y-axis
( ) xxh −=
TransformationsCompare the graph of the function with the graph of ( ) xxf =
(a) Vertical stretch(b) Vertical shrink(c) Horizontal shrink(d) Horizontal stretch(e) Horizontal shift to the right(f) Horizontal shift to the left(g) Vertical shift to the down(h) Vertical shift to the up(i) Reflection on the x-axis(j) Reflection on the y-axis
( ) xxh3
1=
TransformationsCompare the graph of the function with the graph of ( ) xxf =
(a) Vertical stretch(b) Vertical shrink(c) Horizontal shrink(d) Horizontal stretch(e) Horizontal shift to the right(f) Horizontal shift to the left(g) Vertical shift to the down(h) Vertical shift to the up(i) Reflection on the x-axis(j) Reflection on the y-axis
( ) 3−= xxh
TransformationsCompare the graph of the function with the graph of ( ) xxf =
(a) Vertical stretch(b) Vertical shrink(c) Horizontal shrink(d) Horizontal stretch(e) Horizontal shift to the right(f) Horizontal shift to the left(g) Vertical shift to the down(h) Vertical shift to the up(i) Reflection on the x-axis(j) Reflection on the y-axis
( ) xxh −=
TransformationsCompare the graph of the function with the graph of ( ) xxf =
( ) xxh3
1=
(a) Vertical stretch(b) Vertical shrink(c) Horizontal shrink(d) Horizontal stretch(e) Horizontal shift to the right(f) Horizontal shift to the left(g) Vertical shift to the down(h) Vertical shift to the up(i) Reflection on the x-axis(j) Reflection on the y-axis
TransformationsCompare the graph of the function with the graph of ( ) xxf =
(a) Vertical stretch(b) Vertical shrink(c) Horizontal shrink(d) Horizontal stretch(e) Horizontal shift to the right(f) Horizontal shift to the left(g) Vertical shift to the down(h) Vertical shift to the up(i) Reflection on the x-axis(j) Reflection on the y-axis
( ) 3+= xxh
Transformations( ) ( ) 510 2 ++−= xxg
(a) Identify the common function.
(b) Describe the sequence of transformations.
(c) Sketch the graph of g by hand.(d) Use the function notation to write g in
terms of the common function.( ) ( ) 510 ++−= xfxg
Quadratic function
10 units leftReflected on x-axis5 units up
( ) 2xxf =
Transformations( ) ( )31
2
1+−= xxg
(a) Identify the common function.
(b) Describe the sequence of transformations.
(c) Sketch the graph of g by hand.(d) Use the function notation to write g in
terms of the common function.( ) ( )1
2
1+−= xfxg
Cubic function
1 unit leftReflected on x-axisVertical shrink
( ) 3xxf =
Transformations( ) 61 −+−= xxg
(a) Identify the common function.
(b) Describe the sequence of transformations.
(c) Sketch the graph of g by hand.(d) Use the function notation to write g in
terms of the common function.( ) ( ) 61 −+−= xfxg
Square Root function
1 unit leftReflected on x-axis6 units down
( ) xxf =
Transformations( ) 32
2
1−−= xxg
(a) Identify the common function.
(b) Describe the sequence of transformations.
(c) Sketch the graph of g by hand.(d) Use the function notation to write g in
terms of the common function.( ) ( ) 32
2
1−−= xfxg
Absolute value function
2 units to the rightVertical shrink3 units down
( ) xxf =
#51 Transformations( ) ( )252 +−= xxg
(a) Identify the common function.
(b) Describe the sequence of transformations.
(c) Sketch the graph of g by hand.(d) Use the function notation to write g in
terms of the common function.( ) ( )52 +−= xfxg
Quadratic function
5 unit leftReflected on x-axis2 units up
( ) 2xxf =
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