Name: ____________ __________ Period: _______ _______/44 ID: A

1

Math 11 - Functions Test

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. (1 point) The graph of y = −2x + 2| | is

A C

B D

ID: A

2

____ 2. (1 point) The graph of y = (x + 2)2 − 2||

|| is

A C

B D

____ 3. (1 point) Which absolute value function is represented by this graph?

A y = 7x − 21| | C y = −7x − 21| |B y = 7x2 − 21| | D y = 7x2 − 21x| |

ID: A

3

____ 4. (1 point) Which absolute value function is represented by this graph?

A y = 2x2 − 8| | C y = −x2 − 8| |B y = 2x − 8| | D y = 2x2 − 8x| |

____ 5. (1 point) Which graph represents the reciprocal of the linear function y = 4x − 2?

A C

B D

ID: A

4

____ 6. (1 point) Which graph represents the reciprocal of y = 2(x + 2)2 − 3?

A C

B D

ID: A

5

____ 7. (1 point) This is a graph of y = 1f(x) . Determine an equation of the quadratic function y = f(x).

A y = −(x − 1)2 − 9 C y = −(x − 1)2 + 9B y = −(x − 1)2 D y = −x2 + 9

____ 8. (1 point) What is 5(4x2 − y2)

2x2 − 15xy − 8y2 in simplest form? State any non-permissible values.

A5(2x + y)

x − 8y , x ≠ −y2 , x ≠ + 8y C

5(2x − y)x + 8y , x ≠

y2 , x ≠ −8y

B5(2x + y)

x + 8y , x ≠ −y2 , x ≠ −8y D

5(2x − y)x − 8y , x ≠ −

y2 , x ≠ 8y

____ 9. (1 point) Express the product x2 + 6x

2x2 + 15x + 27 × x + 3x2 − 36 in simplest form.

A(x2 + 6x) x + 3� �

(2x2 + 15x + 27)(x2 − 36) C x2x − 36� � x + 6� �

B x2x + 9� � x − 6� �

D − 12x + 9

____ 10. (1 point) Express the quotient x2 − 5x − 24x2 − 11x + 24 ÷ 2x2 + 7x + 3

x2 + x − 12 in simplest form.

A 2x + 1x + 4 C

x + 3� � 2x + 1� �

x − 3� � x + 4� �

B x + 42x + 1 D

x − 3� � x + 4� �

x + 3� � 2x + 1� �

____ 11. (1 point) When fully simplified, ignoring restrictions on the variable, x + 8

x2 + 9x + 20 + x + 5x2 + 7x + 12 is equal to

A 2x + 132x2 + 16x + 32 C 2x2 − 21x − 49

x + 5� � x + 4� � x + 3� �

Bx + 8� � x + 5� �

x2 + 9x + 20� � x2 + 7x + 12� �D 2x2 + 21x + 49

x + 5� � x + 4� � x + 3� �

ID: A

6

____ 12. (1 point) Courtney and Kurtis are planning to travel 60 km in a car by travelling at x kilometres per hour for the first half of the distance, and then increasing their speed by 5 km/h to finish the distance. Which is the correct simplified expression for the total time of the trip?

A 30x + 150x x + 5� �

C 30x + 1502x + 5

B 60x + 1502x + 5 D 60x + 150

x x + 5� �

Short Answer

13. (1 point) Express 64n10m155 in simplified form.

14. (1 point) Simplify 3 175 + 6 63 .

15. (1 point) Express −7 6(−6 5 − 2 6) in simplest form.

16. (1 point) Find a simplified expression for the area of this shape.

3 7 − 4 2

3 7 + 4 2

17. (1 point) Expand and simplify this expression: 3 + 9����

���� 8 3 + 3����

���� − 3 4 3 − 6�

���

����

ID: A

7

18. (1 point) Express 2 21 − 3 7

7+

4 3 − 84

in simplest form.

19. (1 point) Simplify this expression: −8 7 + 5 3

7 − 3

20. (1 point) What are the restrictions on x if the solution to the equation −4 − 4 − x = 6 involves real numbers?

21. (1 point) Solve 2x − 8 = 6x + 3 .

22. (1 point) Solve x − 15 x + 56 = 0.

23. (1 point) Determine the non-permissible values for this rational expression:3n

9n 2 + 3n

ID: A

8

24. (1 point) What is the simplified version of the rational expression −3x + 1232 − 8x

?

25. (1 point) When fully simplified, ignoring non-permissible values, 6x9

3x3 × x8

9x6 is equal to

26. (1 point) When fully simplified, ignoring non-permissible values, 12x12

4x3 ÷ x8

24x6 is equal to

27. (1 point) Simplify. x − 2x + 6 + x + 4

x − 1

28. (1 point) What is the exact solution to the equation 9x + 2x − 9 =2

5

ID: A

9

29. (1 point) Solve dd 2 − 8d − 9

= 5d 2 − 81

30. (1 point) Solve the rational equation x

x + 1 = 4 − xx2 − 3x − 4

+ 6x − 4 .

31. (1 point) Solve 4x − 5 = 6

32. (1 point) Solve x + 4| | = 7.

33. (1 point) Determine the solution(s) to 6x + 9| | + 2 = 8.

ID: A

10

34. (1 point) What is the solution to 4x + 8| | = −8x + 3?

35. (2 points) Solve x2 − 7||

|| = 3.

36. (2 points) Solve. 5h + 2

− 5h − 14h 2 − h − 6

= hh − 3

37. (2 points) Solve x2 + 3x + 3||

|| = 3x + 7.

ID: A

11

38. (4 points) Solve −3x + 1 − 4 = −5x − 1 − 8

.

ID: A

1

Math 11 - Functions TestAnswer Section

MULTIPLE CHOICE

1. D 2. C 3. A 4. A 5. D 6. A 7. B 8. D 9. B 10. B 11. D 12. D

SHORT ANSWER

13. 2n2m3( 25 )

14. 33 7 15. 42 30 + 84 16. 31 17. 39 + 81 3 18. 4 3 − 7

19. −41 − 3 21

4 20. x ≤ 4

21. x = −234

22. x = 64 or x = 49

23. n = 0 and n = −13

24. 38

25. 29x8

26. 72x7

27. 2x2 + 7x + 26(x + 6)(x − 1)

, x ≠ −6, x ≠ 1

28. −2843

ID: A

2

29. a = 1 or a = −5 30. x = 10

31. x = 1214

32. x = 3 or x = −11

33. x = −12 or x = −5

2

34. x = − 512

35. x = ± 10 , x = ±2 36. h = −1 37. x = 2 and –2

38. −3x + 1 − 4 = −5x − 1 − 8

−3x + 1 = −5x − 1 − 4

−3x + 1 = −5x − 1 − 8 −5x − 1 + 16

2x − 14 = −8 −5x − 1

4x2 − 56x + 196 = 64 −5x − 1� �

4x2 − 56x + 196 = −320x − 64

4x2 + 264x + 260 = 0

x =− 264� � ± 264� �

24 4� � 260� �

2 4� �

x = −1, − 65

−3 −1� � + 1 − 4 = −2

−5 −1� � − 1 − 8 = −6

so − 1 is extraneous

−3 −65� � + 1 − 4 = 10

−5 −65� � − 1 − 8 = 10

so − 65 is a solution.