Transformations+of+Trig+Functions+Part+1 PDF

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Precalc...

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Transformations of Trig Functions – Part 1 1) Given the following verbal descriptions, find the transformation rule that you would use to find the new anchor points. Pay attention to order. a)

H. stretch by 3 H. shift left V. flip

 xo , yo   (

___ xo  ___ , ___ yo  ___ )

 xo , yo   (

___ xo  ___ , ___ yo  ___ )



V. shrink by



1 4

V. shift up 1

b)

H. flip H. Shift right  1 H. shrink by 4 V. shift up 3 V. stretch by 5

2) Given the following parent functions and transformation rules, find the equation of the function that results from that anchor point rule. a)

y  sin  x 

 xo , yo   (

 3xo 

 6

, 2 yo  3 )

y  ______________________

b)

y  cos  x 

 xo , yo   (

1  xo  ,  yo  1 ) 2 2

y  ______________________

c)

y  tan  x 

 xo , yo   ( 2  xo  3 

,

2 yo  5 ) 3

y  ______________________

3) Given the following new equations for a transformed function, find the parent function and also find the transformation rule that describes what transformations occurred. a)

y  3cos 5x     2 Parent: ____________

 xo , yo   (

b)

___________ , ____________ )

1 1  y   sin  x  4   1 2 3 

Parent: ____________

 xo , yo   (

c)

___________ , ____________ )

 x   y  4 tan   7  3 

Parent: ____________

 xo , yo   (

___________ , ____________ )

4) Determine what type of linear transformations would affect or change the following characteristics for the sine and cosine functions. Domain: Range: Period and Frequency: Amplitude: Pattern: Midline Equation:

5) Describe how you could use the transformation rule to determine the transformed sine or cosine function characteristics without graphing.  xo , yo   ( 2xo   ,  3 yo  1 ) Domain: Range: Period and Frequency: Amplitude: Pattern: Midline Equation: 6) For each of the following, determine the transformed functions new domain, range, period, frequency, amplitude, midline and new pattern (if pattern changed) without graphing.



a)

y  sin  x 

 xo , yo   (

 3xo 

b)

y  cos  x 

 xo , yo   (

1  xo  ,  y o  1 ) 2 2

6

, 2 yo  3 )

7) For the following, determine the transformed functions new domain, range, period, equations of the asymptotes without graphing. 2 y  tan x   xo , yo   ( 2 xo  6 , yo  5 ) 3

8) Determine the characteristics for the following equations. a) y  2sin  2 x     5

Domain:

Range:

Period and Frequency:

Amplitude:

Pattern:

Midline Equation:

b) y  3cos 5 x     2

Domain:

Range:

Period and Frequency:

Amplitude:

Pattern:

Midline Equation:

9) Determine the transformed functions new domain, range, period, and location of the asymptotes.  x y  4 tan   3

  7 

10) For each of the following parent graphs, list the original anchor points and features from the fundamental period and use the transformation rule to find the new anchor points and features of the transformed function. a) 𝑦 = cos(𝑥)

 xo , yo   (

 3xo 

b) 𝑦 = tan(𝑥)

 xo , yo   (



 6

, 2 yo  3 )

1  xo  ,  yo  2 ) 2 3...