Chapter 5 – RELATIONS AND FUNCTIONS - EXAM REVIEW
Function Fanatic: ______
Section A: Multiple Choice (18 points)
Choose the response that best completes the statement or answers the question.
1. Which set of ordered pairs does not represent a function?
i) ii)
iii) iv)
a. / iv / b. / i / c. / iii / d. / ii2. Identify the range of this relation.
a. / / c. /b. / / d. /
3. This table shows the masses, m grams, of different numbers of identical beads, n. Identify the domain.
a. /b. /
c. /
d. /
Number of Beads,
n / Mass of Beads, m
(g)
1 / 1.56
2 / 3.12
3 / 4.68
4 / 6.24
5 / 7.80
4. Write as an equation in two variables.
a. / / c. /b. / / d. /
5. This graph shows the free-fall speed of a skydiver as a function of time. At what speed was the skydiver
travelling 10 s before she reached the ground?
a. / 10 km/h / b. / 20 km/h / c. / 140 km/h / d. / 30 km/h6. A person in a car drives away from a stop sign, cruises at a constant speed, and then slows down as she n
approaches another stop sign. Which graph best represents this situation?
a. / / c. /b. / / d. /
7. Which of these graphs represents a function?
i) ii)
iii) iv)
a. / i / b. / iii / c. / iv / d. / ii8. Determine the domain and range of the graph of this function.
a. / / c. /b. / / d. /
9. This is a graph of the function . Determine the range value when the domain value is 2.
a. / 7 / b. / 0.5 / c. / 1 / d. / –110. This is a graph of the function . Determine the domain value when the range value is –4.
a. / 11 / b. / 0.5 / c. / –2 / d. / 211. This graph shows the cost of hosting a dance, c, as a function of the number of students attending, n.
What is a restriction on the domain?
a. / The domain can only contain whole numbers that are multiples of 50.b. / The domain can only contain positive numbers.
c. / The domain can only contain whole numbers.
d. / The domain can only contain whole numbers between 1000 and 3500.
12. Which situation represents a linear relation?
i) The number of cells decays at a rate of 12% each day.
ii) A taxi company charges a $3 flat fee plus $1 for each kilometre travelled.
iii) A population of bacteria doubles every hour for 6 h.
iv) An investor’s portfolio increases in value by 6% each year.
a. / ii / b. / iii / c. / iv / d. / i13. This graph shows distance, d kilometres, as a function of time, t minutes. Determine the vertical and
horizontal intercepts.
a. / Vertical intercept: 96Horizontal intercept: 80 / c. / Vertical intercept: 64
Horizontal intercept: 96
b. / Vertical intercept: 80
Horizontal intercept: 96 / d. / Vertical intercept: 80
Horizontal intercept: 64
14. Which graph represents the linear function ?
a. / / c. /b. / / d. /
15. The graph shows the cost of hosting an anniversary party. What is the maximum number of people who
can attend the party for a cost of $1500?
a. / 33 people / c. / 27 peopleb. / 38 people / d. / 61 people
16. Each graph below shows distance, d metres, as a function of time, t hours. Which graph has a rate of
change of 0.75 m/h and a horizontal intercept of 3 m?
a. / / c. /b. / / d. /
17. The distance of line AB given the points A(-2, 5) and B(-4, 8) is:
a. / 2.24 units / c. / 3.61 unitsb. / 1.25 units / d. / 4.20 units
18. The midpoint of points X (-5, 3) and (-7, 5) is:
a. / (-5, 4) / c. / (-1, 1)b. / (-1, 4) / d. / (-6, 4)
Section B: Constructed Response (33 points)
19. (4 points) Here are some families and the number of days they spent camping last summer.
Jones (2); Smith (6); Teynor (9); Glimler (11); Frannot (16)
a) Describe the relation in words.
b) Represent the relation as an arrow diagram.
c) Does this relation represent a function? Explain your answer.
20. (5 points) The equation represents the total cost, C dollars, for a sports banquet when g people attend.
a) Identify the dependent and independent variables.
b) Write the function in function notation.
c) Determine C(46). What does this number represent?
d) Determine the value of g when C(g) = 1581. What does this number represent?
21. (4 points) Sketch a graph of the linear function by finding the x-intercept, the y-intercept, and one additional point.
Time (min) / Distance from Destination (mi.)0 / 285
20 / 244
40 / 203
60 / 162
80 / 121
22. (6 points) A helicopter is travelling toward its destination.
a) Identify the independent and the dependent variables.
b) Use the table of values to determine whether the relation is linear.
c) If the relation is linear, determine its rate of change.
d) Assume the helicopter continues to travel at the same speed. How many more minutes will it take the helicopter to reach its destination? Give your answer to the nearest minute.
e) Graph the data. Will you join the points? Justify your answer.
23. (7 points) This graph shows the distance, d kilometres, from Beijing, China, to Edmonton, Alberta, as a function of flying time, t hours.
a) Determine the vertical and horizontal intercepts.
b) Write the coordinates of the points where the graph intersects
the axes. Describe what the points of intersection represent.
c) Determine the rate of change. What does it represent?
d) Write the domain and range?
e) What is the exact distance to Edmonton when the plane has been
flying for 5 h?
f) Exactly how many hours has the plane been flying when the
distance to Edmonton is 6500 km?
24. (4 points) Plot the points below and calculate the length of each side of triangle XYZ. Classify the triangle as scalene, isosceles, or equilateral.
X(–2, 3), Y(2, 1), Z(–3, –1)
25. (3 points) Point Q(8, -1) is one endpoint and M(5, -5) is the midpoint of a line segment. Determine the coordinate of the other endpoint of the line segment.