Chapter 6 Review

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

Use the graph to answer the question(s) that follow.

The graph shows how the speed of a skier changes over time as she goes down the slope of a mountain.

____	1.	Which statement describes what is happening to the skier as she moves from point C to point D on the graph?
a.	The skier is slowing down and has stopped.	
b.	The skier is travelling at a constant speed.	
c.	The skier has reached her maximum speed.	
d.	The skier is increasing speed at a constant rate.	

____	2.	The graph shows the number of fans for each team who attended basketball games during the playing season. Which team’s attendance is changing at a constant rate?

a.	Both teams	c.	Neither team	
b.	Lizards	d.	Slicers

	

____	3.	Which of the following represent(s) a non-linear relation?

A
	C
	
B

	D

a.	A	c.	C	
b.	A and B	d.	C and D	

____	4.	Which of the following represent(s) a linear relation?

A {(2, 5), (3, 8), (5, 14), (6, 17)}

B

C 

D 

a.	A	c.	C	
b.	A and B	d.	C and D

____	5.	Which scenario can be represented by a discrete relation?
a.	the acceleration a person experiences on the way down a water slide	
b.	the distance travelled by a car travelling at a constant speed	
c.	the population changes of your school over a 5-year period	
d.	the speed of a sky-diver from the time the diver jumps out of a plane to when the diver lands on the ground	

____	6.	Use set notation to state the domain of this function. 

a.		c.		
b.		d.		

____	7.	State the range of this function using set notation.

a.		c.		
b.		d.		

____	8.	Identify the range of the function .
a.		c.		
b.		d.		

____	9.	Which statement describes the domain ?
a.	real numbers greater than or equal to 1 and less than or equal to 3	
b.	real numbers greater than 3 and less than 1	
c.	real numbers greater than or equal to 3 and less than or equal to 1	
d.	real numbers greater than 1 and less than 3	

____	10.	Which statement best describes the domain and range of the equation y = 4x – 6?
a.	The domain and range are both the set of real numbers.	
b.	The domain is the set of real numbers but the range is restricted.	
c.	The range is the set of real numbers but the domain is restricted.	
d.	The domain and range are restricted.	

____	11.	Which relation is not a function?
a.	{(1, 2), (2, 7), (3, 9), (4, 3)}	c.	{(1, 0), (3, 2), (5, 4), (7, 2)}	
b.	{(–2, 1), (0, 4), (2, 9), (4, 16)}	d.	{(3, 4), (6, 8), (9, 5), (3, 3)}	

____	12.	Given the equation f(x) = –6x – 2, determine f(4).
a.	-26	c.	-22	
b.	-24	d.	26	

____	13.	The graph represents the function f(x). What is the value of f(–3)?

a.	1	c.	4	
b.	2	d.	5	

____	14.	Points C(5, 7) and D(–3, –12) are on a line. What is the run from point D to point C?
a.	19	c.	–5	
b.	8	d.	–8	

____	15.	Which of the following relations is not a function?
a.	y = 5x + 3	c.		
b.		d.		

____	16.	Which line segment(s) in the graph has (have) a positive slope?

a.	line segment AB	c.	line segments EF, IJ, and KL	
b.	line segments AB, EF, and CD	d.	line segments IJ, KL, and GH	

Completion  Complete each statement.

	1.	The graph of two quantities that change in relation to each other at a changing rate is represented by a _________________________ .

	2.	A graph whose points are not connected represents _________________________ data.

	3.	A graph of  _________________________ data has no space between points.

	4.	The _________________________ variable depends on another variable.

	5.	_________________________ compares the vertical distance to the horizontal distance between two points on a line. It is represented by the letter _________________________  in the equation of a line and is equal to .

	6.	Points M(2, –8) and N(0, –4) are on a line. 
a) The slope of the line is _________________________ . 
b) The y-intercept of the line is _________________________ .
c) The equation of the line is _________________________ .

Matching      Match each term with the correct definition. A term may be used more than once or not at all.

a.	function	e.	vertical line test	
b.	function notation	f.	x-intercept	
c.	relation	g.	y-intercept	
d.	slope	

____	1.	a measure of the steepness of a line

____	2.	a relation in which any value of the independent variable is related to exactly one value of the dependent variable

____	3.	the point where a line crosses the horizontal axis

____	4.	an association between two quantities

____	5.	a method to determine whether a relation is a function

Short Answer

	1.	The following distance-time graph represents the distance (in kilometres) a person bicycled during a 50-min period. Describe a possible scenario.

	2.	At the bowling alley Angela rented shoes for $3. It cost her $2.50 to bowl each game.
a) Develop an equation that represents the cost of bowling. Use the form , where C(x) is the total cost, and x, is the number of games bowled. Show your thinking.
b) Is this relation a function? Explain.
c) How much did it cost Angela to bowl four games?

	3.	Determine the slope given the rise and the run. 
a) rise = 1, run = 2 
b) rise = 4, run = –1 
c) rise = –3, run = –4 
d) rise = –10, run = –2

	4.	Determine the slope of the line containing each pair of points. 
a) A(0, 5) and B(–3, 2) 
b) C(–2, –3) and D(–6, –11) 
c) E(12, 4) and F(9, 16) 
d) G(–100, 50) and H(–200, 100)

5.  	Use the graph to answer parts a) to d).

a) Identify the coordinates of points C and D. 
b) Identify the rise from point C to point D. 
c) Identify the run from point C to point D. 
d) Identify the slope of the line through points C and D.

	6.	Use the graph to answer parts a) to f).

a) State the coordinates of points E and F. 
b) Determine the rise between points E and F. 
c) Determine the run between points E and F. 
d) Determine the slope of the line containing points E and F.
e) State the y-intercept of the line containing points E and F.
f) State the equation of the line containing points E and F.

Problem

	1.	A flight from Toronto to Rome is modelled by the graph below.

Flight From Toronto to Rome
 
a) Describe what the graph represents.
b) What are the domain and range of the relation that models this situation?
c) How long has the plane been flying when it is 3900 km from Rome? Give your answer to the nearest hour.

	2.	a) Graph the relation given below.
b) Determine the slope of the line.

	3.	Clark earns $40 for every fence he paints. The cost of paint for one fence is $16. Before he started painting he spent a total of $6 for supplies. His profit is equal to his earnings minus all of his expenses. 
a) Make a table of values for 0 to 5 fences painted.
b) Is the relation linear or non-linear? Explain.
c) Graph the relationship. Are the data discrete or continuous?
d) How many fences would Clark have to paint to earn a profit of $210?

	4.	Points A(0, 12) and B(4, –4) are on a line.
a) Plot points A and B and draw the line that passes through them. 
b) Determine the slope of the line. 
c) Make a table of values with x-values from 0 to 4.
Chapter 6 Review
Answer Section

MULTIPLE CHOICE

	1.	ANS:	B	PTS:	1	DIF:	B	OBJ:	Section 6.1

	2.	ANS:	B	PTS:	1	DIF:	A	OBJ:	Section 6.1

	3.	ANS:	D	PTS:	1	DIF:	C	OBJ:	Section 6.2

	4.	ANS:	B	PTS:	1	DIF:	B	OBJ:	Section 6.2

	5.	ANS:	C	PTS:	1	DIF:	B	OBJ:	Section 6.2

	6.	ANS:	B	PTS:	1	DIF:	B	OBJ:	Section 6.3

	7.	ANS:	C	PTS:	1	DIF:	B	OBJ:	Section 6.3

	8.	ANS:	C	PTS:	1	DIF:	D	OBJ:	Section 6.3

	9.	ANS:	D	PTS:	1	DIF:	B	OBJ:	Section 6.3

	10.	ANS:	A	PTS:	1	DIF:	B	OBJ:	Section 6.3
	11.	ANS:	D	PTS:	1	DIF:	B	OBJ:	Section 6.4

	12.	ANS:	A	PTS:	1	DIF:	B	OBJ:	Section 6.4

	13.	ANS:	C	PTS:	1	DIF:	A	OBJ:	Section 6.4

	14.	ANS:	B
Run is the change in horizontal distance, which is the change in the x-coordinates.
run = 5 – (–3)
      = 8

	15.	ANS:	D	PTS:	1	DIF:	C	OBJ:	Section 6.4

	16.	ANS:	C
A line segment with a positive slope slants up from left to right. So, only line segments EF, IJ, and KL have positive slopes.
COMPLETION

	1.	ANS:	curve

	2.	ANS:	discrete

	3.	ANS:	continuous
	4.	ANS:	dependent

	5.	ANS:	Slope; m

	6.	ANS:	
a) –2
b) –4
c) y = –2x – 4
MATCHING
	1.	ANS:	D	PTS:	1	DIF:	B	OBJ:	Section 6.5

	2.	ANS:	A	PTS:	1	DIF:	B	OBJ:	Section 6.4

	3.	ANS:	F	PTS:	1	DIF:	B	OBJ:	Section 6.5

	4.	ANS:	C	PTS:	1	DIF:	B	OBJ:	Section 6.2

	5.	ANS:	E	PTS:	1	DIF:	B	OBJ:	Section 6.4

SHORT ANSWER

	1.	ANS:	
Example:
A cyclist biked away from the starting point at a constant rate for the first 15 min. For the next 15 min, the cyclist pedaled at an increased constant rate. The cyclist then turned around and travelled at a constant speed, returning to the starting point.

	2.	ANS:	
a) In , the fixed cost is $3, so b = 3.
The slope is the rate per game, so m = 2.5.

b) Yes, this is a function because for every value of x there is only one corresponding value for C(x).

c) C(4) = 2.5(4) + 3
    C(4) = 10 + 3
    C(4) = 13
The cost to bowl four games is $13.

	3.	ANS:	
a) 

b)  

c)  

d) 

	4.	ANS:	
a) The slope is 1.
b) The slope is 2.
c) The slope is –4.
d) The slope is .

	5.	ANS:	
a) C(–4, 5), D(2, 5) 
b) rise = 5 – 5
           = 0
The rise is 0.
c) run = 2 – (–4)
           = 6
The run is 6.
d) The slope is 0.

	6.	ANS:	
a) E(–5, –2), F(5, –6)
b) rise = –6 – (–2)
           = –4
The rise is –4.
c) run = 5 – (–5)
           = 10
The run is 10.
d) The slope is .
e) On the graph, the line with E and F crosses the y-axis at –4, so the y-intercept is –4.

f) The equation of the line is .

PROBLEM

	1.	ANS:	
a) The graph represents the distance from its destination of a plane that starts out 7200 km from Rome and flies at a constant speed of 800 km/h until it lands in Rome after 9 h of flying time.

b) Domain: all real numbers between 0 and 9 inclusive
Range: all real numbers between 0 and 7200 inclusive

c) From the graph, the plane is 3900 km from Rome at approximately 4 h. The plane has been flying for approximately 4 h.

	
2.	ANS:	
a)

b) Use two points on the graph to determine the slope, for example, (–6, –12) and (0, –9). 

The slope is .

	3.	ANS:	
a)

b) The relation is linear, because for every increase in the number of fences painted, the profit increases by a constant amount of $24.

c)                                   Fence-Painting Profit 

The data are discrete, as there is no payment for a partially painted fence

d) Extrapolating the graph, we see that Clark would have to paint 9 fences to make $210.

	4.	ANS:	
a)

b)  
 
c)