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Foundations - Chapter Five

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

 1. 

Which graph is the most appropriate to describe a quantity decreasing at a steady rate?
a.
chapterfive_files/i0020000.jpg
c.
chapterfive_files/i0020001.jpg
b.
chapterfive_files/i0020002.jpg
d.
chapterfive_files/i0020003.jpg
 

 2. 

The graph below shows how the cost of gasoline changes over one month. According to the graph, the cost of gasoline ________ decreases.

chapterfive_files/i0030000.jpg
a.
always
b.
sometimes
c.
never
 

 3. 

A function is ________ a relation.
a.
always
b.
sometimes
c.
never
 

 4. 

Identify the mapping diagram that represents the relation and determine whether the relation is a function.
chapterfive_files/i0050000.jpg
a.
chapterfive_files/i0050001.jpg
The relation is not a function.
c.
chapterfive_files/i0050002.jpg
The relation is a function.
b.
chapterfive_files/i0050003.jpg
The relation is a function.
d.
chapterfive_files/i0050004.jpg
The relation is not a function.
 

 5. 

An equation of the form chapterfive_files/i0060000.jpg, where a, b, and c do not equal zero, is ________ a direct variation.
a.
sometimes
b.
always
c.
never
 

 6. 

Lena makes home deliveries of groceries for a supermarket. Her only stops after she leaves the supermarket are at traffic lights and the homes where she makes the deliveries. The graph shows her distance from the store on her first trip for the day. What is the greatest possible number of stops she made at traffic lights?

chapterfive_files/i0070000.jpg
a.
3
b.
4
c.
9
d.
5
 

 7. 

A plane that carries mail makes a round trip each day from Chicago to New York. It makes 3 intermediate stops on the way to New York and 1 intermediate stop on the way back to Chicago. Suppose you make a graph of the altitude of the plane for one day, with time on the horizontal axis and altitude on the vertical axis. How many times will the graph touch the horizontal axis?
a.
11
b.
6
c.
7
d.
4
 

 8. 

Find the domain and range of the relation.

Age of Person
Books Read
65
42
36
37
29
37
29
17
a.
domain: {29, 29, 36}
range: {17, 37, 42}
c.
domain: {29, 36, 65}
range: {37, 37, 42}
b.
domain: {29, 29, 36}
range: {37, 37, 42}
d.
domain: {29, 36, 65}
range: {17, 37, 42}
 

 9. 

Evaluate chapterfive_files/i0100000.jpg for x = 3.
a.
–11
b.
1
c.
–6
d.
11
 

 10. 

Evaluate chapterfive_files/i0110000.jpg for x = 4.
a.
chapterfive_files/i0110001.jpg
b.
chapterfive_files/i0110002.jpg
c.
chapterfive_files/i0110003.jpg
d.
chapterfive_files/i0110004.jpg
 

 11. 

Evaluate chapterfive_files/i0120000.jpg for x = –3.
a.
–9
b.
–4
c.
–8
d.
4
 

 12. 

A taxi company charges passengers $2.00 for a ride, no matter how long the ride is, and an additional $0.20 for each mile traveled. The rule chapterfive_files/i0130000.jpg describes the relationship between the number of miles m and the total cost of the ride c.
a. What is the charge for a 1-mile ride?
b. What is the charge for a 2.7-mile ride?
a.
$2.20; $2.54
b.
$2.00; $2.20
c.
$0.20; $5.60
d.
$0.20; $0.54
 
 
Graph the function.
 

 13. 

chapterfive_files/i0150000.jpg
a.
chapterfive_files/i0150001.jpg
c.
chapterfive_files/i0150002.jpg
b.
chapterfive_files/i0150003.jpg
d.
chapterfive_files/i0150004.jpg
 

 14. 

chapterfive_files/i0160000.jpg
a.
chapterfive_files/i0160001.jpg
c.
chapterfive_files/i0160002.jpg
b.
chapterfive_files/i0160003.jpg
d.
chapterfive_files/i0160004.jpg
 

 15. 

chapterfive_files/i0170000.jpg
a.
chapterfive_files/i0170001.jpg
c.
chapterfive_files/i0170002.jpg
b.
chapterfive_files/i0170003.jpg
d.
chapterfive_files/i0170004.jpg
 
 
Write a function rule for the table.
 

 16. 


x
f(x)
2
–8
3
–12
4
–16
5
–20
a.
chapterfive_files/i0190000.jpg
b.
chapterfive_files/i0190001.jpg
c.
chapterfive_files/i0190002.jpg
d.
chapterfive_files/i0190003.jpg
 

 17. 


x
f(x)
3
7
4
8
5
9
6
10
a.
chapterfive_files/i0200000.jpg
b.
chapterfive_files/i0200001.jpg
c.
chapterfive_files/i0200002.jpg
d.
chapterfive_files/i0200003.jpg
 

 18. 

The length of a field in yards is a function f(n) of the length n in feet. Write a function rule for this situation.
a.
chapterfive_files/i0210000.jpg
b.
chapterfive_files/i0210001.jpg
c.
chapterfive_files/i0210002.jpg
d.
chapterfive_files/i0210003.jpg
 

 19. 

Crystal earns $5.50 per hour mowing lawns.
a. Write a rule to describe how the amount of money m earned is a function of the number of hours h spent mowing lawns.
b. How much does Crystal earn if she works 3 hours and 45 minutes?
a.
chapterfive_files/i0220000.jpg; $61.50
c.
chapterfive_files/i0220001.jpg; $18.98
b.
chapterfive_files/i0220002.jpg; $0.68
d.
chapterfive_files/i0220003.jpg; $20.63
 

 20. 

A zucchini plant in Darnell’s garden was 10 centimeters tall when it was first planted. Since then, it has grown approximately 0.5 centimeters per day.
a. Write a rule to describe the function.
b. After how many days will the zucchini plant be 0.185 meters tall?
a.
chapterfive_files/i0230000.jpg; 17 days
c.
chapterfive_files/i0230001.jpg; 4 days
b.
chapterfive_files/i0230002.jpg; 1.1 days
d.
chapterfive_files/i0230003.jpg; 37 days
 
 
Find the constant of variation k for the direct variation.
 

 21. 

chapterfive_files/i0250000.jpg
a.
k = chapterfive_files/i0250001.jpg
b.
k = chapterfive_files/i0250002.jpg
c.
k = chapterfive_files/i0250003.jpg
d.
k = chapterfive_files/i0250004.jpg
 

 22. 

chapterfive_files/i0260000.jpg
a.
k = chapterfive_files/i0260001.jpg
b.
k = chapterfive_files/i0260002.jpg
c.
k = chapterfive_files/i0260003.jpg
d.
k = chapterfive_files/i0260004.jpg
 

 23. 


x
f(x)
–1
2
0
0
2
–4
5
–10
a.
k = –1.5
b.
k = 2
c.
k = –0.5
d.
k = –2
 

 24. 

The total cost of gasoline varies directly with the number of gallons purchased. Gas costs $1.89 per gallon. Write a direct variation to model the total cost c for g gallons of gas.
a.
chapterfive_files/i0280000.jpg
b.
chapterfive_files/i0280001.jpg
c.
chapterfive_files/i0280002.jpg
d.
chapterfive_files/i0280003.jpg
 

 25. 

The amount of a person’s paycheck p varies directly with the number of hours worked t. For 16 hours of work, the paycheck is $124.00. Write an equation for the relationship between hours of work and pay.
a.
chapterfive_files/i0290000.jpg
b.
chapterfive_files/i0290001.jpg
c.
chapterfive_files/i0290002.jpg
d.
chapterfive_files/i0290003.jpg
 

 26. 

The distance a spring will stretch varies directly with how much weight is attached to the spring. If a spring stretches 9 inches with 100 pounds attached, how far will it stretch with 90 pounds attached? Round to the nearest tenth of an inch.
a.
8.9 in.
b.
10 in.
c.
8.1 in.
d.
9.1 in.
 
 
Use inductive reasoning to describe the pattern. Then find the next two numbers in the pattern.
 

 27. 

–9, –4, 1, 6, . . .
a.
add 5 to the previous term; 11, 16
b.
multiply the previous term by 5; 30, 150
c.
subtract 5 from the previous term; 1, –4
d.
multiply the previous term by 5; 11, 150
 

 28. 

–5, –10, –20, –40, . . .
a.
multiply the previous term by 2; –80, –160
b.
add –5 to the previous term; –35, –30
c.
subtract 5 from the previous term; –80, –160
d.
multiply the previous term by –2; 80, –160
 
 
Find the common difference of the arithmetic sequence.
 

 29. 

9, 13, 17, 21, . . .
a.
4
b.
chapterfive_files/i0350000.jpg
c.
chapterfive_files/i0350001.jpg
d.
22
 

 30. 

5, 5.3, 5.6, 5.9, . . .
a.
0.3
b.
1.1
c.
–1.1
d.
10.3
 

 31. 

2, chapterfive_files/i0370000.jpg, chapterfive_files/i0370001.jpg, chapterfive_files/i0370002.jpg, . . .
a.
chapterfive_files/i0370003.jpg
b.
chapterfive_files/i0370004.jpg
c.
chapterfive_files/i0370005.jpg
d.
chapterfive_files/i0370006.jpg
 

 32. 

The common difference in an arithmetic sequence is ________ a positive number.
a.
sometimes
b.
always
c.
never
 
 
Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.
 

 33. 

chapterfive_files/i0400000.jpg
a.
12, 24, 42
b.
0, 9, 27
c.
3, 24, 27
d.
12, 21, 39
 

 34. 

chapterfive_files/i0410000.jpg
a.
–6, chapterfive_files/i0410001.jpg, chapterfive_files/i0410002.jpg
c.
–6, chapterfive_files/i0410003.jpg, chapterfive_files/i0410004.jpg
b.
0, chapterfive_files/i0410005.jpg, chapterfive_files/i0410006.jpg
d.
5, chapterfive_files/i0410007.jpg, chapterfive_files/i0410008.jpg
 

 35. 

chapterfive_files/i0420000.jpg
a.
–3, –11.8, –25
c.
–3, –9.6, –22.8
b.
0, –6.6, –19.8
d.
–2.2, –11.8, –19.8
 



 
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