IntrotoTransformations&–&Worksheet& MCR3U& Jensen& 2b worksheet package-1.pdf · Answers&! 1)!a)verticalreflectionoverthex 9axisandverticalstretchbafo4! !(−4!)! b)!horizontal!compression!bafo!! - [PDF Document] (2024)

Intro to Transformations – Worksheet MCR3U Jensen 1) Describe the transformations, in order, that are being done to the function f(x). a) g(x)= -­‐4f(x) b) g(x)= f(3x) c) 𝑔 𝑥 = !

!𝑓(−𝑥) d) 𝑔 𝑥 = − !

!𝑓[!

!𝑥 + 1 ]

e) 𝑔 𝑥 = 5𝑓 −2 𝑥 − 4 f) 𝑔 𝑥 = −2𝑓 8𝑥 + 4

h) 𝑔 𝑥 = − !

!𝑓 −3 𝑥 − 1 − 5 i) 𝑔 𝑥 = 4𝑓 − !

!𝑥 + 2 − 1

2) For the graph of f (x) given, sketch the graph of g(x) after the given transformation. a) g(x) = 2f (x) − 2

b) g(x) = ( )1 1 12f x − +

Answers 1) a) vertical reflection over the x-­‐axis and vertical stretch bafo 4 (−4𝑦) b) horizontal compression bafo !

! !

!

c) vertical compression bafo !

! !!, horizontal relection over the y-­‐axis −𝑥

d) vertical reflection over the x-­‐axis and vertical compression bafo !

! !

!!, horizontal stretch bafo 2 2𝑥 ,

phase shift left 1 unit 𝑥 − 1 e) vertical stretch bafo 5 5𝑦 , horizontal reflection over the y-­‐axis and horizontal compression bafo !

!

!!!

, phase shift right 4 units 𝑥 + 4 f) vertical reflection over the x-­‐axis and vertical stretch bafo 2 −2𝑦 , horizontal compression bafo !

! !!,

shift up 4 units 𝑦 + 4 h) vertical reflection over the x-­‐axis and vertical compression bafo !

! !

!!, horizontal reflection over the

y-­‐axis and horizontal compression bafo !! !

!!, phase shift right 1 unit 𝑥 + 1 , shift down 5 units 𝑦 − 5

i) vertical stretch bafo 4 4𝑦 , horizontal reflection over the y-­‐axis and horizontal stretch bafo 2 −2𝑥 , phase shift left 2 units 𝑥 − 2 , shift down 1 unit 𝑦 − 1 2) a) b)

Transformations of Quadratic Functions – Worksheet MCR3U Jensen 1) For each of the following graphs:

i) describe the transformations in order (a à k à d à c) ii) create a table of values for the transformed function iii) graph the transformed function

a) 𝑦 = −𝑥! + 2 b) 𝑦 = 𝑥 − 3 ! + 1

c) 𝑦 = 2𝑥! − 5 d) 𝑦 = −3 𝑥 + 1 !

e) 𝑦 = − 𝑥 + 2 ! + 4 f) 𝑦 = − !

!𝑥!

2) For each function 𝑔(𝑥):

i) describe the transformations from the parent function 𝑓 𝑥 = 𝑥! ii) create a table of values of image points for the transformed function iii) graph the transformed function and write its equation

a) 𝑔(𝑥) = −2𝑓 !

!𝑥 + 2 b) 𝑔(𝑥) = 4𝑓(𝑥 − 3)− 2

c) 𝑦 = 2𝑓(𝑥 + 4)− 3 d) 𝑦 = !

!𝑓 −2 𝑥 + 2 − 3

Transformations of 𝒙 -­‐ Worksheet MCR3U Jensen 1) 1) State the transformations to the parent function 𝑓 𝑥 = 𝑥 in the order that you would do them.

a) g(x) = 2 x +1−3 b) 𝑔 𝑥 = 3 !!(𝑥 − 5)+ 4 c) 𝑔 𝑥 = − !

!−3(𝑥)− 6

2) Graph the parent function, xxf =)( . Describe the transformations in order, make a table of values of image points, write the equation of the transformed function and graph it. a) 𝑔 𝑥 = 𝑓[3 𝑥 + 5 ] b) 𝑔 𝑥 = !

!𝑓(−𝑥)

c) 𝑔 𝑥 = −4𝑓[−2 𝑥 − 3 ]+ 1 3) Use the description to write the transformed function, g(x).

a) The parent function xxf =)( is compressed vertically by a factor of 31 and then translated (shifted) 3 units

left. b) The parent function xxf =)( is reflected over the x-axis, stretch horizontally by a factor of 3 and then translated 1 unit left and 4 units down.

Transformations of 𝟏𝒙 -­‐ Worksheet

MCR3U Jensen 1) State the transformations to the parent function 𝑓 𝑥 = !

! in the order that you would do them.

a) 𝑔 𝑥 = !

!(!!!) b) 𝑔 𝑥 =

−1

𝑥+2− 1 c) 𝑔 𝑥 = !

!!(!!!)

− 0.5

2) Describe the transformations to the parent function 𝑓 𝑥 = !! in order, make a table of values of image points,

write the equation of the transformed function and graph it. a) 𝑔 𝑥 = 𝑓[!

!𝑥 + 1 ] b) 𝑔 𝑥 = 2𝑓(−𝑥)

c) 𝑔 𝑥 = −𝑓[−2 𝑥 − 0.5 ]+ 1 3) Use the description to write the transformed function, g(x).

a) The parent function, 𝑓 𝑥 = !!, is compressed vertically by a factor of

31 and then translated (shifted) 3 units

left. b) The parent function, 𝑓 𝑥 = !

! , is reflected over the x-axis, stretch horizontally by a factor of 3 and then

translated 1 unit left and 4 units down.

2.7 Inverse of a Function – Worksheet MCR3U Jensen 1) Sketch the graph of the inverse of each function. Is the inverse of 𝑓(𝑥) a function? Explain. a) b) 2) Determine the equation of the inverse of each function. a) 𝑓 𝑥 = 2𝑥 b) 𝑓 𝑥 = 6𝑥 − 5 c) 𝑓 𝑥 = !!!!

!

3) Determine the equation of the inverse of each function a) 𝑓 𝑥 = 𝑥! + 6 b) 𝑓 𝑥 = 𝑥 + 8 !

4) For each quadratic function, complete the square and then determine the equation of the inverse. a) 𝑓 𝑥 = 𝑥! + 6𝑥 + 15 b) 𝑓 𝑥 = 2𝑥! + 24𝑥 − 3 5) Determine if the two relations shown are inverses of each other. Justify your conclusion. a) b) 6) For the function 𝑓 𝑥 = −5𝑥 + 6 a) determine 𝑓!!(𝑥) b) Graph 𝑓(𝑥) and its inverse

7) Use transformations to graph the function 𝑓 𝑥 = 2 𝑥 − 2 ! + 1. Find the inverse function 𝑓!!(𝑥) and graph it by reflecting 𝑓(𝑥) over the line 𝑦 = 𝑥 (switch x and y co-ordinates) 8) Determine the equation of the inverse for the given functions and state the domain and range. a) 𝑓 𝑥 = 𝑥 + 3 b) 𝑓 𝑥 = !

!!!+ 2

Answers 1) a) the inverse is NOT a function b) inverse is NOT a function 2) a) 𝑓!! 𝑥 = !

! b) 𝑓!! 𝑥 = !!!

! c) 𝑓!! 𝑥 = !!!!

!

3) a) 𝑓!! 𝑥 = ± 𝑥 − 6 b) 𝑓!! 𝑥 = ± 𝑥 − 8

4) a) 𝑓!! 𝑥 = ± 𝑥 − 6− 3 b) 𝑓!! 𝑥 = ± !!!"!− 6

5) a) yes b) no 6) a) 𝑓!! 𝑥 = !!!!

! b)

7) 𝑓!! 𝑥 = 2± !!!!

8) a) 𝑓!! 𝑥 = 𝑥! − 3; Domain for 𝑓(𝑥): {𝑋 ∈ ℝ|𝑥 ≥ −3}, Range for 𝑓(𝑥): {𝑌 ∈ ℝ|𝑦 ≥ 0} Domain for 𝑓!!(𝑥): {𝑋 ∈ ℝ|𝑥 ≥ 0}, Range for 𝑓(𝑥): {𝑌 ∈ ℝ|𝑦 ≥ −3} b) 𝑓!! 𝑥 = !

!!!+ 2; Domain for 𝑓(𝑥): {𝑋 ∈ ℝ|𝑥 ≠ 2}, Range for 𝑓(𝑥): {𝑌 ∈ ℝ|𝑦 ≠ 2}

Domain for 𝑓!!(𝑥): {𝑋 ∈ ℝ|𝑥 ≠ 2}, Range for 𝑓(𝑥): {𝑌 ∈ ℝ|𝑦 ≠ 2}