Holt McDougal Algebra 1 - sd5.k12.mt.us

27. Round -6.89 to -7, 1.01 to 1 and 4.67 to 5. f(x) = 3x + 5 f(-7) = 3(-7) + 5 = -21 + 5 = -16 f(-6.89) ≈ -16

f(x) = 3x + 5 f(5) = 3(5) + 5 = 15 + 5 = 20 f(4.67) ≈ 20

f(x) = 3x + 5 f(1) = 3(1) + 5 = 3 + 5 = 8 f(1.01) ≈ 8

28a. The number of gallons of gas in the car is between 0 and 20. The domain is 0 ≤ g ≤ 20.

If the car has 0 gallons of gas, the distance it can travel is d = 30(0) = 0. If the car has 20 gallons of gas, it can travel d = 30(20) = 600. The range is

0 ≤ d ≤ 600.

b. d = 30g d = 30(12) = 360 The car can travel 360 miles on 12 gallons of gas.

29. Possible answer: There can be a maximum of 4 bowlers on each bowling lane, and each bowler needs to rent 2 shoes.

30. Rashid must multiply $150 by the number of months he saves for, not add the number of months to $150.

31. Possible answer: The cost of a hotel room is a function of how many nights you stay. The cost is the dependent variable because it depends on the number of nights, therefore, the number of nights is the independent variable.

32a. 1250(0) = 0 1250(1) = 1250 1250(2) = 2500 1250(3) = 3750 1250(4) = 5000 The value of v is 1250 times the value of t. v = 1250t

b. Independent variable: time Dependent variable: volume

c. v = 1250t 10,000 = 1250t

10,000

______ 1250

= 1250t _____ 1250

8 = t The pool takes 8 hours to fill.

teSt prep

33. D; it costs $0.10 for the pencil and $0.70x for all the pens. The total cost is the sum of the two.

34. G; notice that 5.25(5) = 26.25, 5.25(10) = 52.50, and 5.25(15) = 78.75. So G is correct.

35. 3.5

f(x) = 5 - 1 __ 2 x

f(3) = 5 - 1 __ 2 (3)

= 5 - 1.5 = 3.5

challenge and extend

36. Since the temperature in Celsius is between 0 and 100, the domain is 0 ≤ x ≤ 100.

f(x) = 9 __ 5 x + 32

f(0) = 9 __ 5 (0) + 32

= 0 + 32 = 32

f(x) = 9 __ 5

x + 32

f(100) = 9 __ 5

(100) + 32

= 180 + 32 = 212

The temperature in Fahrenheit is between 32 and 212. So the range is 32 ≤ f(x) ≤ 212.

37. The acceleration due to gravity in meters per second squared is 9.8 m/ s 2 .

d = 1 __ 2 g t 2

d = 1 __ 2 (9.8)(3 ) 2

= 4.9(9) = 44.1 The object will fall 44.1 meters in 3 seconds.

GrAphinG Functions

CheCk it out!

1a. -2x + y = 3 _______ +2x ____ +2x y = 2x + 3

x y = 2x + 3 (x, y)

-5 y = 2(-5) + 3 = -7 (-5, -7)

-3 y = 2(-3) + 3 = -3 (-3, -3)

1 y = 2(1) + 3 = 5 (1, 5)

4 y = 2(4) + 3 = 11 (4, 11)

8

4

-4

x

y

0 2 4 -2 -4

b. x f(x) = x 2 + 2 (x, f(x))

-3 f(x) = (-3 ) 2 + 2 = 11 (-3, 11)

-1 f(x) = (-1 ) 2 + 2 = 3 (-1, 3)

0 f(x) = (0 ) 2 + 2 = 2 (0, 2)

1 f(x) = (1 ) 2 + 2 = 3 (1, 3)

3 f(x) = (3 ) 2 + 2 = 11 (3, 11)

2 -2

4

6

8

10

2

x

y

0

79 Holt McDougal Algebra 1 79 Holt McDougal Algebra 1

3-4

CS10_A1_MESK710372_C03.indd 79 3/30/11 10:43:17 PM

2a. x f(x) = 3x - 2 (x, f(x))

-2 f(x) = 3(-2) - 2 = -8 (-2, -8)

-1 f(x) = 3(-1) - 2 = -5 (-1, -5)

0 f(x) = 3(0) - 2 = -2 (0, -2)

1 f(x) = 3(1) - 2 = 1 (1, 1)

2 f(x) = 3(2) - 2 = 4 (2, 4)

Draw a line through all the points to show all ordered pairs that satisfy the function. Draw arrowheads on both “ends” of the line.

-2

x y

0 2 -2

b. x y = |x - 1| (x, y)

-2 y = |-2 - 1| = 3 (-2, 3)

-1 y = |-1 - 1| = 2 (-1, 2)

0 y = |0 - 1| = 1 (0, 1)

1 y = |1 - 1| = 0 (1, 0)

2 y = |2 - 1| = 1 (2, 1)

3 y = |3 - 1| = 2 (3, 2)

4 y = |4 - 1| = 3 (4, 3)

Draw a V through all the points to show all ordered pairs that satisfy the function. Draw arrowheads on the “ends” of the V.

4

x

y

0 2 4 -2

3. Locate 3 on the y-axis. Move right to the graph of the function. Then move down to the x-axis to find the corresponding value of x.

x = 3

4. x y = 6x (x, y)

0 y = 6(0) = 0 (0, 0)

1 y = 6(1) = 6 (1, 6)

2 y = 6(2) = 12 (2, 12)

3 y = 6(3) = 18 (3, 18)

4 y = 6(4) = 24 (4, 24)

Average Speed of Lava Flow

0 1 2 3 4 5

10

20

30

Time (h)

Dis

tanc

e (m

i)

Use the graph to estimate the y-value when x is 5.5. The lava moved about 33 miles.

think and disCuss

1. Possible answer: Graph the function by plotting points and connecting them with a line or smooth curve. Then use the graph to determine all possible values of y (the range).

2. Locate the given value on the x-axis. Move up the graph of the function and then left or right to the y-axis to find the y-value.

3.

Real-world situation: Use a domain that makessense in the given situation. Choose some values for x, and use the function to find corresponding values for y. Plot the points and,if it makes sensein the situation, connect them with a line or smooth curve.

Not a real-worldsituation: Use a domain of all real numbers. Choose some values for x, and use the function to findcorresponding values for y. Plot the points and connect them with a line or smooth curve.

Graphing a Function

exerCisesguided practice

1. 3x - y = 1 _______ -3x ____ -3x -y = -3x + 1 -1(-y) = -1(-3x + 1) y = 3x - 1

x y = 3x - 1 (x, y)

-3 y = 3(-3) - 1 = -10 (-3, -10)

-1 y = 3(-1) - 1 = -4 (-1, -4)

0 y = 3(0) - 1 = -1 (0, -1)

4 y = 3(4) - 1 = 11 (4, 11)

8

4

-8

x

y

0 4 8 -4 -8


CS10_A1_MESK710372_C03.indd 80 3/30/11 10:43:19 PM

2. x f(x) = -|x| (x, f(x))

-5 f(x) = -|-5| = -5 (-5, -5)

-3 f(x) = -|-3| = -3 (-3, -3)

0 f(x) = -|0| = 0 (0, 0)

3 f(x) = -|3| = -3 (3, -3)

5 f(x) = -|5| = -5 (5, -5)

-4

-2

-6

x y

0 4 2 -4 -2

3. x f(x) = x + 4 (x, f(x))

-5 f(x) = -5 + 4 = -1 (-5, -1)

-3 f(x) = -3 + 4 = 1 (-3, 1)

0 f(x) = 0 + 4 = 4 (0, 4)

4 f(x) = 4 + 4 = 8 (4, 8)

4

6

2

x

y

0 4 2 -2

4. x y = x 2 - 1 (x, y)

-3 y = (-3 ) 2 - 1 = 8 (-3, 8)

-1 y = (-1 ) 2 - 1 = 0 (-1, 0)

0 y = (0 ) 2 - 1 = -1 (0, -1)

1 y = (1 ) 2 - 1 = 0 (1, 0)

3 y = (3 ) 2 - 1 = 8 (3, 8)

4

6

2

x

y

0 4 2 -4 -2

5. x f(x) = 6x + 4 (x, f(x))

-2 f(x) = 6(-2) + 4 = -8 (-2, -8)

-1 f(x) = 6(-1) + 4 = -2 (-1, -2)

0 f(x) = 6(0) + 4 = 4 (0, 4)

1 f(x) = 6(1) + 4 = 10 (1, 10)


4

2

x

y

0 2 -2

6. x y = 1 __ 2 x - 4 (x, y)

-4 y = 1 __ 2 (-4) - 4 = -6 (-4, -6)

-2 y = 1 __ 2 (-2) - 4 = -5 (-2, -5)

0 y = 1 __ 2 (0) - 4 = -4 (0, -4)

2 y = 1 __ 2 (2) - 4 = -3 (2, -3)

4 y = 1 __ 2 (4) - 4 = -2 (4, -2)


2

x

y

0 2 -2

7. x + y = 0 ______ -x ___ -x y = -x

x y = -x (x, y)

-3 y = -(-3) = 3 (-3, 3)

-2 y = -(-2) = 2 (-2, 2)

-1 y = -(-1) = 1 (-1, 1)

0 y = -(0) = 0 (0, 0)

1 y = -(1) = -1 (1, -1)

2 y = -(2) = -2 (2, -2)

3 y = -(3) = -3 (3, -3)


2

-2

x

y

0 2 -2


CS10_A1_MESK710372_C03.indd 81 3/30/11 10:43:22 PM

8. x y = |x| - 4 (x, y)

-6 y = |-6| - 4 = 2 (-6, 2)

-4 y = |-4| - 4 = 0 (-4, 0)

-2 y = |-2| - 4 = -2 (-2, -2)

0 y = |0| - 4 = -4 (0, -4)

2 y = |2| - 4 = -2 (2, -2)

4 y = |4| - 4 = 0 (4, 0)

Draw a V through the points to show all ordered pairs that satisfy the function. Draw arrowheads on both “ends” of the V.

4

2

-2

-4

x

y

0 2 -2 -4

9. x f(x) = 2 x 2 - 7 (x, f(x))

-3 f(x) = 2(-3 ) 2 - 7 = 11 (-3, 11)

-2 f(x) = 2(-2 ) 2 - 7 = 1 (-2, 1)

-1 f(x) = 2(-1 ) 2 - 7 = -5 (-1, -5)

0 f(x) = 2(0 ) 2 - 7 = -7 (0, -7)

1 f(x) = 2(1 ) 2 - 7 = -5 (1, -5)

2 f(x) = 2(2 ) 2 - 7 = 1 (2, 1)

3 f(x) = 2(3 ) 2 - 7 = 11 (3, 11)

Draw a smooth curve through all the points to show all ordered pairs that satisfy the function. Draw arrowheads on both “ends” of the curve.

-2

x y

0 4 -2 -4

10. x y = - x 2 + 5 (x, y)

-2 y = -(-2 ) 2 + 5 = 1 (-2, 1)

-1 y = -(-1 ) 2 + 5 = 4 (-1, 4)

0 y = -(-0 ) 2 + 5 = 5 (0, 5)

1 y = -(1 ) 2 + 5 = 4 (1, 4)

2 y = -(2 ) 2 + 5 = 1 (2, 1)


-2

2

6

x

y

0 4 2 -4

11. Locate 2 on the x-axis. Move down to the graph of the function. Then move left to the y-axis to find the corresponding value of y.

y = -1

12. x y = x (x, y)

0 y = 0 (0, 0)

1 y = 1 (1, 1)

2 y = 2 (2, 2)

3 y = 3 (3, 3)

4 y = 4 (4, 4)

Atlantic Ocean Floor Spreading

0 2 4 6 8 10

2

4

6

8

10

Time (yr)

Dis

tanc

e sp

read

ing

(in.)

Use the graph to estimate the y-value when x is 10.5.

The ocean floor will spread about 10.5 inches.


CS10_A1_MESK710372_C03.indd 82 3/30/11 10:43:24 PM

practice and problem Solving

13. 2x + y = 4 _______ -2x ____ -2x y = -2x + 4

x y = -2x + 4 (x, y)

-3 y = -2(-3) + 4 = 10 (-3, 10)

-1 y = -2(-1) + 4 = 6 (-1, 6)

4 y = -2(4) + 4 = -4 (4, -4)

7 y = -2(7) + 4 = -10 (7, -10)

8

4

-8

-4

x

y

0 8 4 -8 -4

14. x y = |x| - 1 (x, y)

-4 y = |-4| - 1 = 3 (-4, 3)

-2 y = |-2| - 1 = 1 (-2, 1)

0 y = |0| - 1 = -1 (0, -1)

2 y = |2| - 1 = 1 (2, 1)

4 y = |4| - 1 = 3 (4, 3)

4

2

-2

x

y

0 4 2 -4 -2

15. x f(x) = -7x (x, f(x))

-2 f(x) = -7(-2) = 14 (-2, 14)

-1 f(x) = -7(-1) = 7 (-1, 7)

0 f(x) = -7(0) = 0 (0, 0)

1 f(x) = -7(1) = -7 (1, -7)

8

12

4

-4

x

y

0 2 4 -2 -4

16. x y = (x + 1) 2 (x, y)

-2 y = (-2 + 1) 2 = 1 (-2, 1)

-1 y = (-1 + 1) 2 = 0 (-1, 0)

0 y = (0 + 1) 2 = 1 (0, 1)

1 y = (1 + 1) 2 = 4 (1, 4)

2 y = (2 + 1) 2 = 9 (2, 9)

4

6

8

2

x

y

0 4 2 -4 -2

17. x y = -3x + 5 (x, y)

-1 y = -3(-1) + 5 = 8 (-1, 8)

0 y = -3(0) + 5 = 5 (0, 5)

1 y = -3(1) + 5 = 2 (1, 2)

2 y = -3(2) + 5 = -1 (2, -1)

3 y = -3(3) + 5 = -4 (3, -4)


4

2

x

y

0 4

18. x f(x) = 3x (x, f(x))

-2 f(x) = 3(-2) = -6 (-2, -6)

-1 f(x) = 3(-1) = -3 (-1, -3)

0 f(x) = 3(0) = 0 (0, 0)

1 f(x) = 3(1) = 3 (1, 3)

2 f(x) = 3(2) = 6 (2, 6)


2

x

y

0 2 -2


CS10_A1_MESK710372_C03.indd 83 3/30/11 10:43:27 PM

19. x + y = 8 ______ -x ___ -x y = -x + 8

x y = -x + 8 (x, y)

-2 y = -(-2) + 8 = 10 (-2, 10)

0 y = -(0) + 8 = 8 (0, 8)

2 y = -(2) + 8 = 6 (2, 6)

4 y = -(4) + 8 = 4 (4, 4)

6 y = -(6) + 8 = 2 (6, 2)

8 y = -(8) + 8 = 0 (8, 0)

10 y = -(10) + 8 = -2 (10, -2)


4

8

x

y

0 4 8 -2

20. x f(x) = 2x + 2 (x, f(x))

-2 f(x) = 2(-2) + 2 = -2 (-2, -2)

-1 f(x) = 2(-1) + 2 = 0 (-1, 0)

0 f(x) = 2(0) + 2 = 2 (0, 2)

1 f(x) = 2(1) + 2 = 4 (1, 4)

2 f(x) = 2(2) + 2 = 6 (2, 6)


2

4

x

y

0 2 -2

21. x y = -|x| + 10 (x, y)

-6 y = -|-6| + 10 = 4 (-6, 4)

-4 y = -|-4| + 10 = 6 (-4, 6)

-2 y = -|-2| + 10 = 8 (-2, 8)

0 y = -|0| + 10 = 10 (0, 10)

2 y = -|2| + 10 = 8 (2, 8)

4 y = -|4| + 10 = 6 (4, 6)

6 y = -|6| + 10 = 4 (6, 4)


4

y

0 8 4 -8 -4

22. x f(x) = -5 + x 2 (x, f(x))

-3 f(x) = -5 + (-3 ) 2 = 4 (-3, 4)

-2 f(x) = -5 + (-2 ) 2 = -1 (-2, -1)

-1 f(x) = -5 + (-1 ) 2 = -4 (-1, -4)

0 f(x) = -5 + (0 ) 2 = -5 (0, -5)

1 f(x) = -5 + (1 ) 2 = -4 (1, -4)

2 f(x) = -5 + (2 ) 2 = -1 (2, -1)

3 f(x) = -5 + ( 3) 2 = 4 (3, 4)


-2

x y

0 -3 3

23. x y = |x + 1| + 1 (x, y)

-4 y = |-4 + 1| + 1 = 4 (-4, 4)

-3 y = |-3 + 1| + 1 = 3 (-3, 3)

-2 y = |-2 + 1| + 1 = 2 (-2, 2)

-1 y = |-1 + 1| + 1 = 1 (-1, 1)

0 y = |0 + 1| + 1 = 2 (0, 2)

1 y = |1 + 1| + 1 = 3 (1, 3)

2 y = |2 + 1| + 1 = 4 (2, 4)


4

2

x

y

0 2 -4 -2


CS10_A1_MESK710372_C03.indd 84 3/30/11 10:43:30 PM

24. x y = (x - 2 ) 2 - 1 (x, y)

-1 y = (-1 - 2 ) 2 - 1 = 8 (-1, 8)

0 y = (0 - 2 ) 2 - 1 = 3 (0, 3)

1 y = (1 - 2 ) 2 - 1 = 0 (1, 0)

2 y = (2 - 2 ) 2 - 1 = -1 (2, -1)

3 y = (3 - 2 ) 2 - 1 = 0 (3, 0)

4 y = (4 - 2 ) 2 - 1 = 3 (4, 3)

5 y = (5 - 2 ) 2 - 1 = 8 (5, 8)


4

2

x

y

0 4

25. Locate -4 on the x-axis. Move up to the graph of the function. Then move right to the y-axis to find the corresponding value of y.

y = 5

26. Locate 6 on the x-axis. Move up to the graph of the function. Then move left to the y-axis to find the corresponding value of y.

y = 3

27. x y = 0.25x (x, y)

0 y = 0.25(0) = 0 (0, 0)

4 y = 0.25(4) = 1 (4, 1)

8 y = 0.25(8) = 2 (8, 2)

12 y = 0.25(12) = 3 (12, 3)

16 y = 0.25(16) = 4 (16, 4)

Electric Scooter Mileage

0 4 8 12

1

2

3

Time (min)

Dis

tanc

e (m

i)

Use the graph to estimate the y-value when x is 15. An electric scooter travels about 3.75 miles in

15 min.

28. x f(x) = x - 1 (x, f(x))

-2 f(x) = -2 - 1 = -3 (-2, -3)

-1 f(x) = -1 - 1 = -2 (-1, -2)

0 f(x) = 0 - 1 = -1 (0, -1)

1 f(x) = 1 - 1 = 0 (1, 0)

2 f(x) = 2 - 1 = 1 (2, 1)

3 f(x) = 3 - 1 = 2 (3, 2)

4 f(x) = 4 - 1 = 3 (4, 3)


2

-4

x

y

0 4 2 -2

29. 12 - x - 2y = 0 ___________ -12 ____ -12 -x - 2y = -12 _______ +x ____ +x -2y = x - 12

-2y

____ -2

= x - 12 ______ -2

y = - 1 __ 2 x + 6

x y = - 1 __ 2 x + 6 (x, y)

-2 y = - 1 __ 2 (-2) + 6 = 7 (-2, 7)

0 y = - 1 __ 2 (0) + 6 = 6 (0, 6)

2 y = - 1 __ 2 (2) + 6 = 5 (2, 5)

4 y = - 1 __ 2 (4) + 6 = 4 (4, 4)

6 y = - 1 __ 2 (6) + 6 = 3 (6, 3)


4

2

x

y

0 4 2


CS10_A1_MESK710372_C03.indd 85 3/30/11 10:43:32 PM

30. 3x - y = 13 _______ -3x ____ -3x -y = -3x + 13 -1(-y) = -1(-3x + 13) y = 3x - 13

x y = 3x - 13 (x, y)

-1 y = 3(-1) - 13 = -16 (-1, -16)

0 y = 3(0) - 13 = -13 (0, -13)

1 y = 3(1) - 13 = -10 (1, -10)

2 y = 3(2) - 13 = -7 (2, -7)

3 y = 3(3) - 13 = -4 (3, -4)

4 y = 3(4) - 13 = -1 (4, -1)

5 y = 3(5) - 13 = 2 (5, 2)


-4

-8

-12

x y 0 8

31. x y = x 2 - 2 (x, y)

-3 y = (-3 ) 2 - 2 = 7 (-3, 7)

-2 y = (-2 ) 2 - 2 = 2 (-2, 2)

-1 y = (-1 ) 2 - 2 = -1 (-1, -1)

0 y = (0 ) 2 - 2 = -2 (0, -2)

1 y = (1 ) 2 - 2 = -1 (1, -1)

2 y = (2 ) 2 - 2 = 2 (2, 2)

3 y = (3 ) 2 - 2 = 7 (3, 7)


2

4

-2

x

y

0 2 -2

32. x 2 - y = -4 _______ - x 2 ____ - x 2 -y = - x 2 - 4

-1(-y) = -1 (- x 2 - 4) y = x 2 + 4

x y = x 2 + 4 (x, y)

-3 y = (-3 ) 2 + 4 = 13 (-3, 13)

-2 y = (-2 ) 2 + 4 = 8 (-2, 8)

-1 y = (-1 ) 2 + 4 = 5 (-1, 5)

0 y = (0 ) 2 + 4 = 4 (0, 4)

1 y = (1 ) 2 + 4 = 5 (1, 5)

2 y = (2 ) 2 + 4 = 8 (2, 8)

3 y = (3 ) 2 + 4 = 13 (3, 13)


8

12

x

y

0 2 -2

33. x f(x) = 2 x 2 (x, f(x))

-2 f(x) = 2(-2 ) 2 = 8 (-2, 8)

-1 f(x) = 2(-1 ) 2 = 2 (-1, 2)

0 f(x) = 2(0 ) 2 = 0 (0, 0)

1 f(x) = 2(1 ) 2 = 2 (1, 2)

2 f(x) = 2(2 ) 2 = 8 (2, 8)


4

x

y

0 2 -2


CS10_A1_MESK710372_C03.indd 86 3/30/11 10:43:34 PM

34. x f(x) = |2x| - 2 (x, f(x))

-3 f(x) = |2(-3)| - 2 = 4 (-3, 4)

-2 f(x) = |2(-2)| - 2 = 2 (-2, 2)

-1 f(x) = |2(-1)| - 2 = 0 (-1, 0)

0 f(x) = |2(0)| - 2 = -2 (0, -2)

1 f(x) = |2(1)| - 2 = 0 (1, 0)

2 f(x) = |2(2)| - 2 = 2 (2, 2)

3 f(x) = |2(3)| - 2 = 4 (3, 4)


4

2

-2

x

y

2 -2

35. x y = -|x| (x, y)

-3 y = |- (-3) | = 3 (-3, 3)

-2 y = |- (-2) | = 2 (-2, 2)

-1 y = |- (-1) | = 1 (-1, 1)

0 y = |- (0) | = 0 (0, 0)

1 y = |- (1) | = 1 (1, 1)

2 y = |- (2) | = 2 (2, 2)

3 y = |- (3) | = 3 (3, 3)


4

2

x

y

0 2 -2

36. x y = -|2x + 1| (x, y)

-3 y = -|2(-3) + 1| = -5 (-3, -5)

-2 y = -|2(-2) + 1| = -3 (-2, -3)

-1 y = -|2(-1) + 1| = -1 (-1, -1)

0 y = -|2(0) + 1| = -1 (0, -1)

1 y = -|2(1) + 1| = -3 (1, -3)

2 y = -|2(2) + 1| = -5 (2, -5)


x y

2 -2 -4

-4

37. Use a graph of the function. Locate 12 on the y-axis. Move right to the graph of the function. Then move down to the x-axis to find the corresponding value of x.

x = 1

38. Use a graph of the function. Locate 6 on the y-axis. Move left to the graph of the function. Then move down to the x-axis to find the corresponding value of x.

x = -10

39. Use a graph of the function. Locate -2 on the x-axis. Move down to the graph of the function. Then

move right to the y-axis to find the corresponding value of y.

y = -8

40. __________ y = 7x - 2 5 7(1) - 2 5 7 - 2 5 5 3

___________ y = 7x -2 10 7(2) - 2 10 14 - 2 10 12 7

(1, 5) is on the graph but (2, 10) is not.

41. _________ y = |x| + 2 5 |3| + 2 5 3 + 2 5 5 3

___________ y = |x| + 2 3 |-1| + 2 3 1 + 2 3 3 3

Both (3, 5) and (-1, 3) are on the graph.

42. _______ y = x 2 1 (1 ) 2 1 1 3

_________ y = x 2 -9 (- 3) 2 -9 9 7

(1, 1) is on the graph but (-3, -9) is not.

43. ___________

y = 1 __ 4 x - 2

- 3 __ 4 1 __

4 (1) - 2

- 3 __ 4 1 __

4 - 8 __

4

- 3 __ 4 - 7 __

4 7

___________

y = 1 __ 4

x - 2

-1 1 __ 4

(4) - 2

-1 1 - 2 -1 -1 3

(4, -1) is not on the graph but (1, - 3 __ 4

) is.

44. Student A; student A substituted the coordinates of the ordered pair incorrectly, and student B substituted them correctly.

45. _______________ x + 3y = -11 0 + 3(-7) -11 0 - 21 -11 -21 -11 7

_________________ x + 3y = -11

-6 + 3 (- 5 __ 3

) -11

-6 - 5 -11 -11 -11 3

________________ x + 3y = -11 -2 + 3(-3) -11 -2 - 9 -11 -11 -11 3

(-6, - 5 __ 3

) and (-2, -3)

are on the graph but (0, -7) is not.


CS10_A1_MESK710372_C03.indd 87 3/30/11 10:43:37 PM

46. _____________ y + |x| = -1 -7 + |0| -1 -7 + 0 -1 -7 -1 7

______________ y + |x| = -1

- 5 __ 3 + |-6| -1

- 5 __ 3 + 6 -1

13 ___ 3 -1 7

_______________ y + |x| = -1 -3 + |-2| -1 -3 + 2 -1 -1 -1 3

(-2, -3) is on the graph but (0, -7) and

(-6, - 5 __ 3 ) are not.

47. ______________ x 2 - y = 7 (0 ) 2 - (-7) 7 0 + 7 7 7 7 3

________________ x 2 - y = 7

(-6 ) 2 - (- 5 __ 3 ) 7

36 + 5 __ 3 7

113 ____ 3

7 7

_______________ x 2 - y = 7 (- 2) 2 - (-3) 7 4 + 3 7 7 7 3

(0, -7) and (-2, -3) are on the graph but

(-6, - 5 __ 3 ) is not.

48. -6 = 3x + 2y ____ -3x ________ -3x -3x - 6 = 2y

-3x - 6 _______ 2 =

2y ___

2

- 3 __ 2 x - 3 = y

y = - 3 __ 2 x - 3

x y = - 3 __ 2 x - 3 (x, y)

-2 y = - 3 __ 2 (-2) - 3 = 0 (-2, 0)

0 y = - 3 __ 2 (0) - 3 = -3 (0, -3)

2 y = - 3 __ 2 (2) - 3 = -6 (2, -6)

Possible answer: (-2, 0), (0, -3), (2, -6)

49. x y = 1.1x + 2 (x, y)

-1 y = 1.1(-1) + 2 = 0.9 (-1, 0.9)

0 y = 1.1(0) + 2 = 2 (0, 2)

1 y = 1.1(1) + 2 = 3.1 (1, 3.1)

Possible answer: (-1, 0.9), (0, 2), (1, 3.1)

50. x y = 4 __ 5 x (x, y)

-1 y = 4 __ 5 (-1) = - 4 __

5 (-1, - 4 __

5 )

0 y = 4 __ 5 (0) = 0 (0, 0)

1 y = 4 __ 5 (1) = 4 __

5 (1, 4 __

5 )

Possible answer: (-1, - 4 __ 5 ) , (0, 0), (1, 4 __

5 )

51. x y = 3x - 1 (x, y)

-2 y = 3(-2) - 1 = -7 (-2, -7)

0 y = 3(0) - 1 = -1 (0, -1)

1 y = 3(1) - 1 = 2 (1, 2)

Possible answer: (-2, -7), (0, -1), (1, 2)

52. x y = |x| + 6 (x, y)

0 y = |0| + 6 = 6 (0, 6)

1 y = |1| + 6 = 7 (1, 7)

2 y = |2| + 6 = 8 (2, 8)

Possible answer: (0, 6), (1, 7), (2, 8)

53. x y = x 2 - 5 (x, y)

-1 y = (-1 ) 2 - 5 = -4 (-1, -4)

0 y = (0 ) 2 - 5 = -5 (0, -5)

1 y = (1 ) 2 - 5 = -4 (1, -4)

Possible answer: (-1, -4), (0, -5), (1, -4)

54. Possible answer: The graphs are alike because they are both V-shaped. They are different because the graph of y = |x| opens upward and the graph of y = -|x| opens downward.

55a. v = 10,000 - 1500h

b. v = 10,000 - 1500h v = 10,000 - 1500(1) v = 10,000 - 1500 v = 8500 There is 8500 gallons of water in the pool after

1 hour.

c. Time (h)

Volume (gal)

0 10,000

1 8,500

2 7,000

3 5,500

4 4,000

Draining Swimming Pool

Time (h)

Volu

me

(gal

)

0

2000 3000

1000

4000 5000 6000 7000 8000 9000

10000

3 4 5 6 7 2 1

56. Round 2.117 to 2. Locate 2 on the x-axis. Move down to the graph of the function. Then move left to the y-axis to find the corresponding value of y.

y ≈ -2


CS10_A1_MESK710372_C03.indd 88 3/30/11 10:43:39 PM

57. The graph can represent all ordered pairs that satisfy the function, even when there are infinitely many.

teSt prep

58. A; Since (-2, -2), (0, 1), and (4, 7) all satisfy 2y - 3x = 2, the line must be A.

59. J; Since 4 - |3| = 4 - 3 = 1 ≠ -1, (3, -1) is not on the graph.

60. C; Since - 2 __ 3 (3) + 4 = -2 + 4 = 2, (3, 2) is on the

graph of y = - 2 __ 3 x + 4.

61. J; Since a real number squared is always positive,

x 2 is positive so x 2 + 1 is positive. So all points are above the origin I is true. Since x-values can be positive or negative, II is false. Since all points are above the origin, all y-values are positive so, III is true.

challenge and extend

62. x y = x 3 (x, y)

-2 y = (-2 ) 3 = -8 (-2, -8)

-1 y = (-1 ) 3 = -1 (-1, -1)

0 y = (0 ) 3 = 0 (0, 0)

1 y = (1 ) 3 = 1 (1, 1)

2 y = (2 ) 3 = 8 (2, 8)


2

x

y

0 2 -2

63. Let x represent the number of hours and let y represent the temperature.

y = 4x + 64

x y = 4x + 64 (x, y)

0 y = 4(0) + 64 = 64 (0, 64)

2 y = 4(2) + 64 = 72 (2, 72)

4 y = 4(4) + 64 = 80 (4, 80)

6 y = 4(6) + 64 = 88 (6, 88)

8 y = 4(8) + 64 = 96 (8, 96)

10 y = 4(10) + 64 = 104 (10, 104)

0

40

60

80

100

4 6 8 2

Liquid Temperature

Time (h)

Tem

pera

ture

( ˚F)

reAdY to Go on? section A Quiz

1. graph B 2. graph A

3. Quiz Score

0 1 2 3 4

20

60 40

80

Problems missed

Scor

e

4. Domain: {-1, 0, 1}; Range: {2, 3, 4} Not a function; the x-value 0 is assigned to the

y-value 3 and the y-value 4.

5. Domain: {-2, 0, 2}; Range: {3} Function; each element in the domain is assigned to

exactly one element in the range.

6. Domain: -4 ≤ x ≤ 2; Range: 0 ≤ y ≤ 4 Function; each element in the domain is assigned to

exactly one element in the range.

7. 1 - 7 = -6 2 - 7 = -5 3 - 7 = -4 4 - 7 = -3 The value of y is 7 less than x. y = x - 7

8. -3(1) = -3 -3(2) = -6 -3(3) = -9 -3(4) = -12 The value of y is -3 times the value of x. y = -3x

9. Independent variable: minutes Dependent variable: pages Let m represent the number of minutes. f(m) = 8m

10. f(x) = 3x - 1 f(2) = 3(2) - 1 = 6 - 1 = 5

11. g(x) = x 2 - x g(-2) = (-2 ) 2 - (-2) = 4 + 2 = 6

12. f(x) = 15 + 3x The number of poses must be a whole number.

A reasonable domain is {1, 2, 3, 4, 5}.

x 1 2 3 4 5

f(x) 18 21 24 27 30

So a reasonable range is {18, 21, 24, 27, 30}.


CS10_A1_MESK710372_C03.indd 89 3/30/11 10:43:42 PM

13. 2x - y = 3 _______ -2x ____ -2x -y = -2x + 3 -1(-y) = -1(-2x + 3) y = 2x - 3

x y = 2x - 3 (x, y)

-2 y = 2(-2) - 3 = -7 (-2, -7)

0 y = 2(0) - 3 = -3 (0, -3)

1 y = 2(1) - 3 = -1 (1, -1)

3 y = 2(3) - 3 = 3 (3, 3)

2

-6

-2

-4

x

y

0 4 2 -4 -2

14. x y = 4 - x 2 (x, y)

-1 y = 4 - (-1 ) 2 = 3 (-1, 3)

0 y = 4 - (0 ) 2 = 4 (0, 4)

1 y = 4 - (1 ) 2 = 3 (1, 3)

2 y = 4 - (2 ) 2 = 0 (2, 0)

4

-2

x

y

0 2 -2

15. x y = 3 - 2x (x, y)

-1 y = 3 - 2(-1) = 5 (-1, 5)

0 y = 3 - 2(0) = 3 (0, 3)

1 y = 3 - 2(1) = 1 (1, 1)

3 y = 3 - 2(3) = -3 (3, -3)

2

-2

x

y

0 4 -2

16. x + y = 6 ______ -x ___ -x y = -x + 6

x y = -x + 6 (x, y)

0 y = -(0) + 6 = 6 (0, 6)

1 y = -(1) + 6 = 5 (1, 5)

2 y = -(2) + 6 = 4 (2, 4)

3 y = -(3) + 6 = 3 (3, 3)

4 y = -(4) + 6 = 2 (4, 2)

5 y = -(5) + 6 = 1 (5, 1)

6 y = -(6) + 6 = 0 (6, 0)


4

6

2

x

y

0 2 4 6

17. x y = |x| - 3 (x, y)

-3 y = |-3| - 3 = 0 (-3, 0)

-2 y = |-2| - 3 = -1 (-2, -1)

-1 y = |-1| - 3 = -2 (-1, -2)

0 y = |0| - 3 = -3 (0, -3)

1 y = |1| - 3 = -2 (1, -2)

2 y = |2| - 3 = -1 (2, -1)

3 y = |3| - 3 = 0 (3, 0)


2

-4

y

0 3 -3 x


CS10_A1_MESK710372_C03.indd 90 3/30/11 10:43:44 PM

18. x y = x 2 + 1 (x, y)

-3 y = (- 3) 2 + 1 = 10 (-3, 10)

-2 y = (-2 ) 2 + 1 = 5 (-2, 5)

-1 y = (-1 ) 2 + 1 = 2 (-1, 2)

0 y = (0 ) 2 + 1 = 1 (0, 1)

1 y = (1 ) 2 + 1 = 2 (1, 2)

2 y = (2 ) 2 + 1 = 5 (2, 5)

3 y = (3 ) 2 + 1 = 10 (3, 10)


4

6

x

y

0 2 -2

19. x y = 8x (x, y)

0 y = 8(0) = 0 (0, 0)

2 y = 8(2) = 16 (2, 16)

4 y = 8(4) = 32 (4, 32)

6 y = 8(6) = 48 (6, 48)

8 y = 8(8) = 64 (8, 64)

Speed of Storm

0 4 8 12

10 20 30 40 50 60 70 80

Time (h)

Dis

tanc

e (m

i)

90

Use the graph to estimate the y-value when x is 10.5.

The storm travels about 85 miles in 10.5 hours.

scAtter plots And trend lines

CheCk it out!

1.

0

5 10 15 20 25 30 35 40 45

4 3 2 1

Football Team Scores

Game

Poin

ts s

core

d

2. positive correlation

3a. No correlation; the temperature in Houston has nothing to do with the number of cars sold in Boston.

b. Positive correlation; as the number of family members increases, more food is needed, so the grocery bill increases too.

c. Negative correlation; as the number of times you sharpen your pencil increases, the length of the pencil decreases.

4. Graph A; it cannot be graph B because graph B shows negative minutes; it cannot be graph C because graph C shows the temperature of the pie increasing, a positive correlation.

5. Based on the data, about 75 paper rolls need to be sold to raise $500.

think and disCuss

1. No; no correlation means that there is no relationship and the points on the graph show no pattern.

2.

NegativeCorrelation

NoCorrelation

PositiveCorrelation

Graph Example

Possible answer: the total price of an ice cream cone and the number of scoops

The amount of water in a watering can and the number of flowers watered.

Possible answer: the number of magazines a person has and the size of the person’s shoes

exerCisesguided practice

1. Possible answer: a circle graph

2. Possible answer: A graph with a negative correlation shows one set of values decreasing as the other set increases, while a graph with no correlation shows no relationship.

3. No; a trend line just fits the pattern of the data points, so it usually does not pass through every point.

4. Garden Statues

Height (in.)

Pric

e ($

)

0

10 20 30 40 50 60 70 80 90

20 10 40 30

5. positive correlation 6. negative correlation


3-5

CS10_A1_MESK710372_C03.indd 91 3/30/11 10:43:47 PM

Holt McDougal Algebra 1 - sd5.k12.mt.us

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