Identify the transformations and write using function notation

Name: ________________________

MCR3U – WS – Transformations & Graphing of Exponential Functions

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Write each of the following using x-y notation (i.e., y  a b  k x  p

    q)

1. y  h x  5   3, given h x   2x

2. y  3g x  5   1, given g x   4x

3. y  f 1 3

x  5  



  5, given f x   4x

4. y  h 1 4

x  3  



  3, given h x   5x

5. y  f  x  2    

    5, given f x   4

x

6. y  1 4 g

1 3

x  4  



  3, given g x   5x

7. y  3h 1 2

x 



  5, given h x   5x

8. y  f 1 3

x  2  



  4, given f x   5x

9. y  3h 1 2

x  4  



  1, given h x   2x

Identify the transformations and write using function notation (i.e., y  af k x  p   

  

    q ). Be sure to specify the

parent function, f x   bx .

10. y  5 2  1

3 x  4 

 4

11. y  2 3  1 2

x  3   1

12. y  2 2  1 2

x  1   2

13. y  5 2  1

2 x  3 

 1

14. y  3 2  1 2

x  3 

15. y  3 2  1 5

x  3   4

Graph the following using transformations (if possible using integer values). Sketch otherwise.

16. y  1 5

g 4 x  3    

    3, given g x   2

x

17. y  h 1 4

x  4  



  5, given h x   2x

18. y  2g  x  2    

    2, given g x   2

x

19. y  3g 3 x  2    

    4, given g x   2

x

20. y  h x  1   4, given h x   2x

21. y  2h 1 5

x  3  



  4, given h x   2x

22. y  1 4

g 2 x  1    

    3, given g x   2

x

23. y  3f 3 x  4    

    4, given f x   2

x

 

 

Name: _______________ WS – Rational Functions – Order of Operations Mar 25, 2019

Simplify and state and restrictions:

1. 3 x+ 1 2 x– 3

+ x

x 2−9

2. 3 x

x 2+ 3 x+ 2

− 4 x

x 2+ 5 x+ 6

+ 5 x

x 2+ 4 x+ 3

3. 3 x

6 x 2 – x−2

+ 2 x

10 x 2 – x−3

4. x+ 1

2 x 2 – 7 x+ 6

− x –3

2 x 2 – x−3

5. 3 x

6 x 2+ 13 x– 5

+ 2 x+ 1

6 x 2 + 7 x−3

6. x– 2

6 x 2 – 7 x– 5

÷ 2 x

3 x 2 –5 x

− 3 x+ 2

2 x 2+ 11 x+ 5

Name: _______________ WS – Rational Functions – Order of Operations Mar 25, 2019

Simplify and state and restrictions:

1. 3 x+ 1 2 x– 3

+ x

x 2−9

2. 3 x

x 2+ 3 x+ 2

− 4 x

x 2+ 5 x+ 6

+ 5 x

x 2+ 4 x+ 3

3. 3 x

6 x 2 – x−2

+ 2 x

10 x 2 – x−3

4. x+ 1

2 x 2 – 7 x+ 6

− x –3

2 x 2 – x−3

5. 3 x

6 x 2+ 13 x– 5

+ 2 x+ 1

6 x 2 + 7 x−3

6. x– 2

6 x 2 – 7 x– 5

÷ 2 x

3 x 2 –5 x

− 3 x+ 2

2 x 2+ 11 x+ 5

 

 

Name: ________________________ Date: ______________________

Ver: A # Pages: 1

MPM2D – Worksheet – Factoring Complex Trinomials (with Common Factors)

1. 3x 2

+ 25x + 8

2. 5x 2

+ 46x + 9

3. 2x 2

+ 15x + 22

4. 3x 2

+ 14x + 15

5. 8x 2

+ 22x + 5

6. 2x 2

+ 7x + 3

7. 5x 2

+ 61x + 12

8. 8x 2

+ 46x + 11

9. 6x 2

+ 11x + 3

10. 8x 2

+ 38x + 9

11. −4x 2

+ 2x + 72

12. 12x 2

− 117x − 30

13. 20x 2

− 42x + 16

14. 12x 2

+ 69x − 105

15. 50x 2

+ 140x + 80

16. −20x 2

− 230x + 120

17. 15x 2

− 70x − 25

18. 6x 2

− 22x − 84

19. 18x 2

+ 87x − 66

20. 100x 2

− 170x − 110

21. −6x 2

− 44x + 160

22. −3x 2

− 4x + 20

23. 4x 2

+ 17x + 18

24. 24x 2

+ 20x − 100

25. 20x 2

+ 29x + 5

26. 75x 2

− 170x − 385

27. 30x 2

− 129x − 198

28. 2x 2

+ 13x + 20

29. 5x 2

+ 14x + 8

30. 20x 2

− 150x + 280

31. 10x 2

+ 106x − 44

32. 20x 2

+ 13x + 2

33. 4x 2

+ 15x + 14

34. 2x 2

+ 11x + 9

35. 25x 2

− 70x + 40

36. 5x 2

+ 11x + 6

37. 5x 2

+ 13x + 8

38. 20x 2

+ 88x − 192

39. −8x 2

− 66x − 70

 

 

MCR 3U Function Notation Date:

Fill in the table. Simplify the functions f(x) = x and f(x) = x2 so that they are in the form y=mx+ b and y=a(x–h)2+ k . Do your rough work (where necessary) on a separate page.

f (x) x x2 √x 1 x

1. 5 f (a)

2. – f (a)

3. f (a)+ 4

4. f (a)– 6

5. f (a+ 2)

6. f (a –1)

7. f (3a)

8. f (–a)

9. f (– 2a)

10. f ( a2) 11. f [ 3(a– 1)]

12. f (– 3a)+ 6

13. – 2 f (a– 6)+ 4

14. 5 f [ 4(a –1)]– 3

15. 3a– 6

16. 3a2 – 4

17. −√3−a

18. 1 a+ 2

−1

19. –5(a– 2)2+7

20. 3√4a−8−2

21. −3 a−5

+2

Answers from #15-21 may vary.

 

 

MCR3U Worksheet – Graphs of Parent Functions Feb 27, 2019

The Quadratic Function: y=x2 The Absolute Value Function: y=∣x∣

x y

-3

-2

-1

0

1

2

3

x

y x y

-3

-2

-1

0

1

2

3

x

y

Domain: Domain:

Range: Range:

Max/Min (if any): Max/Min (if any):

The Radical Function: y=x The Reciprocal Function: y= 1 x

x y

-1

0

1

4

9

x

y x y

-2

-1

-0.5

0

0.5

1

2

x

y

Domain: Domain:

Range: Range:

Max/Min (if any): Max/Min (if any):

Asymptotes (if any): Asymptotes (if any):

rev 24. Sep. 2012 Text: McGraw-HIll Ryerson Mathematics 11 (2001)

 

 

Name: ________________________ Class/Period: __________ Attempt # _____ Date: 01/31/2012 ID: A

y = ax 2

+ bx + c y = a(x − r)(x − s) y = a(x − h) 2

+ k x = −b ± b

2 − 4ac

2a D = b

2 − 4ac

Proficiency Demonstrated: Perfect ���� Sufficient ���� Insufficient (Repeat Evaluation) ����

MPM2D – Essential Skills Proficiency Assessment # 3 – Quadratic Properties, Expanding, and Factoring

1. Determine the key features of the provided graph and record them in the table.

Direction of Opening

Number of Zeroes

Location of Zeroes

y-intercept

Axis of Symmetry

Max/Min Value

Vertex

2. Expand and simplify (x + 4)(5x − 4)

3. Fully factor x 2

− 3x − 18

4. Determine the y-intercept, zeroes, equation of the

axis of symmetry, and the vertex of:

y = (x + 10)(x − 12)

 

 

Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Practice – Rational Expressions

1. x + 5

x 2

+ 5x + 4 −

x + 4

x 2

+ 13x + 36

2. x + 3

x 2

+ 3x − 28 +

x − 6

x 2

+ x − 20

3. x + 5

x 2

− 11x + 30 +

x + 6

x 2

− 12x + 35

4. x + 3

x 2

− 2x − 35 −

x − 4

x 2

− 14x + 49

5. x + 2

x 2

− 7x + 6 −

x + 7

x 2

− 6x + 5

6. x − 7

x 2

− 4 −

x − 9

x 2

− 5x − 14

7. x + 2

x 2

− 16x + 63 +

x + 7

x 2

− 7x − 18

8. x − 8

x 2

− 3x − 28 −

x − 8

x 2

− 49

9. x + 5

x 2

− x − 56 +

x − 6

x 2

− 4x − 32

10. x − 5

x 2

− 3x − 54 +

x − 1

x 2

+ 8x + 12

11. x + 7

x 2

+ 6x + 5 −

x + 5

x 2

− 3x − 4

12. x − 5

x 2

+ x − 42 −

x − 8

x 2

− x − 56

13. x + 8

x 2

− 8x + 16 −

x − 2

x 2

− 3x − 4

14. x − 3

x 2

+ x − 12 −

x + 7

x 2

− 16

15. x − 9

x 2

+ 7x + 12 +

x − 6

x 2

+ 6x + 8

16. x − 2

x 2

− 13x + 36 −

x + 5

x 2

− x − 72

17. x

2 + x − 20

x 2

+ 2x − 35 ÷

x 2

− 3x − 4

x 2

− 14x + 45

18. x

2 + 2x − 48

x 2

+ 8x − 9 ÷

x 2

+ 2x − 48

x 2

+ 7x − 18

19. x

2 + 15x + 54

x 2

− x − 12 ×

x 2

+ 3x − 28

x 2

+ 15x + 54

20. x

2 − x − 56

x 2

+ 2x − 3 ×

x 2

− 4x + 3

x 2

+ 6x − 7

21. x

2 − 7x + 12

x 2

+ 8x + 15 ÷

x 2

− 11x + 24

x 2

+ x − 6

22. 6x

2 − 2x − 48

3x 2

+ 5x − 28 ×

x 2

+ 6x + 8

4x 2

− 18x + 18

23. 5x

2 + 34x − 7

4x 2

− 24x ×

12x 2

+ 24x

3x 2

+ 15x − 42

24. x

2 + 6x + 8

x 2

+ 8x + 15 ÷

4x 2

+ 13x + 10

2x 2

+ 2x − 40

25. x

2 − 36

9x 2

+ 3x ×

3x 2

+ 25x + 8

4x 2

− 26x + 12

26. x

2 + 7x − 8

8x 2

− 16x + 6 ÷

x 2

− 64

20x 2

+ 10x − 10

27. 4x

2 − 24x − 64

3x 2

+ 21x + 30 ÷

4x 2

+ 16x + 16

9x 2

+ 30x + 24

28. 8x

2 + 36x

15x 2

− 4x − 4 ×

25x 2

+ 35x + 10

12x 2

+ 28x

29. 2x

2 − 8x − 24

6x 2

− 5x − 56 ÷

x 2

− 5x − 6

2x 2

+ 11x − 63

30. 12x

2 + 53x + 56

x 2

+ 4x − 45 ÷

3x 2

+ 17x + 24

x 2

− 5x

31. x

2 + x − 42

x 2

− 2x − 35 ×

4x 2

+ 24x + 20

5x 2

+ 34x − 7

 

 

Name: ________________________ Date: 10/21/2013 ID: A

COMMUNICATION No Level 0 1 2 3 4 5 6 7 8 9 10

Page 1 of 1Conventions & Terminology No level assigned based on content of this page

Unacceptable Few Major / Many Minor Errors Few Minor Errors No Errors

Expression & Organization Significant Improvements Required Few Improvements Required No Improvements Required

MCR3U – WS – Radicals

1. Write each as a mixed radical (a b ) in simplest

form:

a) −4 18 b) 7 125

2. Write each as a mixed radical (a b ) in simplest

form:

a) 112 b) −9 50

3. Write each as a mixed radical (a b ) in simplest

form:

a) 5 12 b) 32

4. Write each as a mixed radical (a b ) in simplest

form:

a) 6 48 b) −4 8

5. Write each as a mixed radical (a b ) in simplest

form:

a) 4 27 b) −8 72

6. Write each as an entire radical ( a ):

a) 8 3 b) −7 2

7. Write each as an entire radical ( a ):

a) 6 2 b) −6 3

8. Write each as an entire radical ( a ):

a) −4 7 b) 12 3

9. Write each as an entire radical ( a ):

a) 10 2 b) −9 3

10. Simplify:

6 128 + 6 108 + 10 75 − 5 50

11. Simplify:

−7 125 + 8 112 + 9 63 − 7 20

12. Simplify:

8 18 − 10 48 − 6 12 + 3 50

13. Simplify:

2 12 + 6 80 − 7 20 − 2 108

14. Simplify:

6 72 − 3 12 − 48 − 5 128

15. Simplify:

2 128 − 7 45 − 2 20 − 8

16. Simplify 8

175