MCR3U - Exam Review

Multiple Choice Identify the choice that best completes the statement or answers the question.

____ 1. Which of the following relations is not a function?

a.

c.

b.

d.

____ 2. Which graph is not a function? a.

c.

b.

d.

____ 3. Which relation is not a function? a. {(–13, –10), (–15, –12), (–11, –8), (–16, 4)} b. {(8, 17), (5, 5), (8, –3), (4, –1)} c. {(–14, –2), (–10, 6), (–1, 3), (10, 6)} d. {(0, –2), (–4, 6), (4, 15), (12, 6)}

____ 4. Evaluate for . a. –20 c. 20 b. 6 d. 34

____ 5. The graph of is shown.

Evaluate g(2). a. –2 c. 1 b. 0 d. 4

____ 6. Consider the functions and . Which of the following is true? a. c. b. d.

____ 7. Evaluate for . a. –6 c. 26 b. 3 d. 94

____ 8. The graph of is shown.

Evaluate h(–1) + h(4). a. –14 c. –3 b. –12 d. 0

____ 9. What is the domain of the relation shown?

a. {–3, –2, 0, 1, 2, 4} c. { I} b. { } d. {–4, –1, 0, 2, 3, 5}

____ 10. What are the domain and range of the function ? a. Domain = { R}

Range = { R} c. Domain = { R }

Range = { R } b. Domain = { R }

Range = { R } d. Domain = { R | }

Range = { R }

____ 11. What are the domain and range of the relation that contains the points {(–16, –10), (–14, –8), (–11, –3), (–7, 4), (–1, –8)}? a. Domain = {–16, –14, –11, –10, –8, –7, –3, –1, 4}

Range = {–16, –14, –11, –10, –8, –7, –3, –1, 4} b. Domain = {–10, –8, –3, 4}

Range = {–16, –14, –11, –7, –1} c. Domain = {–16, –14, –11, –7, –1}

Range = {–10, –8, –3, 4} d. Domain = { }

Range = { }

____ 12. There is a bacteria cell in a Petri dish. The cell reproduces at a rate of per hour for 10 hours. What are the domain and range of the function? a. Domain = { R }

Range = { R } c. Domain = { }

Range = { } b. Domain = { }

Range = { } d. Domain = { R }

Range = { R }

____ 13. What are the domain and range of the function ? a. Domain = { R}

Range = { R } c. Domain = { R}

Range = { R } b. Domain = { R}

Range = { R } d. Domain = { R}

Range = { R}

____ 14. Which of the following is the inverse to the function ? a.

c.

b.

d.

____ 15. A graph of a relation is shown.

Which of the following is the graph of the inverse?

a.

c.

b.

d.

____ 16. Which of the following is the inverse relation to the set of ordered pairs {(–10, 5), (–7, 9), (0, 6), (8, –12)}? a. {(5, –10), (9, –7), (6, 0), (–12, 8)} c. {(10, –5), (7, –9), (0, –6), (–8, 12)} b. {(–10, –5), (–7, –9), (0, –6), (8, 12)} d. {(–5, 10), (–9, 7), (–6, 0), (12, –8)}

____ 17. Which of the following is the inverse to the function ? a.

c.

b.

d.

____ 18. A graph of a function is shown.

Which of the following is the graph of the inverse? a.

c.

b.

d.

____ 19. Which of the following is the parent function for ?

a. c. b. d.

____ 20. The solid graph has been compressed horizontally by the factor relative to the dotted graph of .

Which of the following is the equation for the solid graph?

a. c. b.

d.

____ 21. Which of the following is the parent function for ?

a. c. b. d.

____ 22. Which of the following transformations is required to graph from its parent function? a. Reflect the graph in the x-axis, then translate it 6 units to the left. b. Reflect the graph in the y-axis, then translate it 6 units to the right. c. Reflect the graph in the y-axis, then translate it 6 units to the left. d. Reflect the graph in the x-axis, then translate it 6 units to the right.

____ 23. The point (2, 6) is on the graph of . What are the coordinates of the image of this point on the graph ?

a. (8, 24) c.

b. (8, 6) d.

____ 24. Which of the following is NOT a transformation that can be used to graph the function from the parent function? a. Vertical translation 2 units up b.

Horizontal compression by a factor of

c. Reflection in the x-axis

d. Horizontal translation 4 units to the right

____ 25. Which of the following is a transformation that can be used to graph the function ? a. Vertical translation 12 units up b. Horizontal stretch by the factor 5 c. Reflection in the y-axis d. Horizontal translation 9 units to the right

____ 26. Which of the following is the graph of the function ? (The parent function is dotted.) a.

c.

b.

d.

____ 27. Which of the following is the equation for the graph shown?

a. c. b. d.

____ 28. For , which of the following is the graph of ? a.

c.

b.

d.

____ 29. Which of the following is the graph of the function ? (The parent function is dotted.)

a.

c.

b.

d.

____ 30. Which of the following is the equation for the graph shown?

a. c. b. d.

____ 31. For , which of the following is the graph of ?

a.

c.

b.

d.

MCR3U - Exam Review Answer Section

MULTIPLE CHOICE

1. ANS: C PTS: 1 REF: Knowledge and Understanding

OBJ: 1.1 - Relations and Functions

2. ANS: C PTS: 1 REF: Knowledge and Understanding OBJ: 1.1 - Relations and Functions

3. ANS: B PTS: 1 REF: Knowledge and Understanding OBJ: 1.1 - Relations and Functions

4. ANS: D PTS: 1 REF: Knowledge and Understanding OBJ: 1.2 - Function Notation

5. ANS: D PTS: 1 REF: Knowledge and Understanding OBJ: 1.2 - Function Notation

6. ANS: D PTS: 1 REF: Knowledge and Understanding OBJ: 1.2 - Function Notation

7. ANS: A PTS: 1 REF: Knowledge and Understanding OBJ: 1.2 - Function Notation

8. ANS: A PTS: 1 REF: Knowledge and Understanding OBJ: 1.2 - Function Notation

9. ANS: A PTS: 1 REF: Knowledge and Understanding OBJ: 1.4 - Determining the Domain and Range of a Function

10. ANS: D PTS: 1 REF: Knowledge and Understanding OBJ: 1.4 - Determining the Domain and Range of a Function

11. ANS: C PTS: 1 REF: Knowledge and Understanding OBJ: 1.4 - Determining the Domain and Range of a Function

12. ANS: B PTS: 1 REF: Thinking OBJ: 1.4 - Determining the Domain and Range of a Function

13. ANS: B PTS: 1 REF: Knowledge and Understanding OBJ: 1.4 - Determining the Domain and Range of a Function

14. ANS: D PTS: 1 REF: Knowledge and Understanding OBJ: 1.5 - The Inverse Function and Its Properties

15. ANS: C PTS: 1 REF: Knowledge and Understanding OBJ: 1.5 - The Inverse Function and Its Properties

16. ANS: A PTS: 1 REF: Knowledge and Understanding OBJ: 1.5 - The Inverse Function and Its Properties

17. ANS: C PTS: 1 REF: Knowledge and Understanding OBJ: 1.5 - The Inverse Function and Its Properties

18. ANS: B PTS: 1 REF: Application OBJ: 1.5 - The Inverse Function and Its Properties

19. ANS: C PTS: 1 REF: Knowledge and Understanding OBJ: 1.7 - Investigating Horizontal Stretches, Compressions, and Reflections

20. ANS: D PTS: 1 REF: Knowledge and Understanding OBJ: 1.7 - Investigating Horizontal Stretches, Compressions, and Reflections

21. ANS: D PTS: 1 REF: Knowledge and Understanding OBJ: 1.7 - Investigating Horizontal Stretches, Compressions, and Reflections

22. ANS: C PTS: 1 REF: Thinking

OBJ: 1.7 - Investigating Horizontal Stretches, Compressions, and Reflections

23. ANS: D PTS: 1 REF: Thinking OBJ: 1.7 - Investigating Horizontal Stretches, Compressions, and Reflections

24. ANS: B PTS: 1 REF: Knowledge and Understanding OBJ: 1.8 - Using Transformations to Graph Functions of the Form y = af[k(x - d)] + c

25. ANS: A PTS: 1 REF: Knowledge and Understanding OBJ: 1.8 - Using Transformations to Graph Functions of the Form y = af[k(x - d)] + c

26. ANS: C PTS: 1 REF: Knowledge and Understanding OBJ: 1.8 - Using Transformations to Graph Functions of the Form y = af[k(x - d)] + c

27. ANS: C PTS: 1 REF: Application OBJ: 1.8 - Using Transformations to Graph Functions of the Form y = af[k(x - d)] + c

28. ANS: C PTS: 1 REF: Application OBJ: 1.8 - Using Transformations to Graph Functions of the Form y = af[k(x - d)] + c

29. ANS: C PTS: 1 REF: Knowledge and Understanding OBJ: 1.8 - Using Transformations to Graph Functions of the Form y = af[k(x - d)] + c

30. ANS: D PTS: 1 REF: Application OBJ: 1.8 - Using Transformations to Graph Functions of the Form y = af[k(x - d)] + c

31. ANS: B PTS: 1 REF: Application OBJ: 1.8 - Using Transformations to Graph Functions of the Form y = af[k(x - d)] + c