Trig - 11/27/2015 LO: Nonrigid Transformations Compare the graphs of the three functions. Describe...

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



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f x( ) = x + 3

A. Shift left

B. Shift right

C. Shift up

D. Shift down



€

f x( ) = x − 4

Nonrigid Transformations

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f x( ) = ax 2

€

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


( ) xxf =


( ) xxh4

1=

|b| < 1inside


( ) 3xxf =


( ) ( )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



( ) xxh 3=



( ) xxh −=



( ) xxh3

1=



( ) 3−= xxh



( ) xxh −=


( ) xxh3

1=




( ) 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




terms of the common function.( ) ( )1

2

1+−= xfxg

Cubic function

1 unit leftReflected on x-axisVertical shrink

( ) 3xxf =

Transformations( ) 61 −+−= xxg




terms of the common function.( ) ( ) 61 −+−= xfxg

Square Root function

1 unit leftReflected on x-axis6 units down

( ) xxf =

Transformations( ) 32

2

1−−= xxg




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




terms of the common function.( ) ( )52 +−= xfxg

Quadratic function

5 unit leftReflected on x-axis2 units up

( ) 2xxf =

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Trig - 11/27/2015 LO: Nonrigid Transformations Compare the graphs of the three functions. Describe...

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