ame: ________________________
MCR3U – WS – Transformations & Graphing of Exponential Functions
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
17. Simplify 98
245
18. Simplify 125
20
19. Simplify 343
27
20. Simplify 2 7 − 2 2
4 35 − 5 10
21. Simplify 2 21 − 14
−4 21 − 3 14
22. Simplify − 7
− 7 − 5
23. Simplify − 10 − 5 15
4 2 − 3 3
Name: ________________________ 10/30/2019 ID: A
MCR3U – WS – Transformations & Graphing of Exponential Functions
Determine the exponential equation given:
1. (a) common ratio 2. (b) horizontal asymptote at y 7. (c) y-intercept of –2.
2. (a) common ratio 1
3 .
(b) horizontal asymptote at y 3. (c) y-intercept of –7.
3. (a) common ratio 2. (b) horizontal asymptote at y 6. (c) y-intercept of –3.
4. (a) common ratio 1
5 .
(b) horizontal asymptote at y 17. (c) y-intercept of 21.
Determine the exponential equation for each of the following graphs:
5.
6.
7.
8.
ID: A
9.
10.
11.
12.
Rewrite the following using only vertical transformations (i.e., in the form y a b x q).
13. y 2 4 3 x 2 4
14. y 4 32 1 5
x 1 4
15. y 2 9 1 2
x 4 1
16. y 5 625 1
4 x 5
3
Determine the equation of the exponential function corresponding to the following points.
17. (–2, 169), (–3, 49), (–4, 29), (–5, 77 3
)
18. (–11, 31 6
), (–7, 67 6
), (–3, 79 6
), (1, 83 6
)
19. (20, 19 2
), (15, 7 2
), (10, 1 2
), (5, 1)
20. (5, 14), (3, 16), (1, 21), (–1, 131 6
)
