1) f(x) = x2 – 3 x + 2. The domain of f(x) is {1, 3, 5, 7}. Find the range.

f(1) = 1 – 3 + 2 = 0 f(3) = 9 – 9 + 2 = 2 f(5) = 25 – 15 + 2 = 12 f(7) = 49 – 21 + 2 = 30

{0, 2, 12, 30}

2) Jack has only quarters and nickels in his pocket. He has a total of $ 1.50 in his pocket. Assume that quarters are the domain. What are all possible members of the domain?

{0, 1, 2, 3, 4, 5, 6}

3) A hot tub contains 1200 gallons and is being drained. Every hour the volume decreases by 60 gallons.

a) Write an equation that models this situation.

c) Identify the practical domain and range.

b) Identify the independent and dependent variables.

y = 1200 – 60 x

independent: x: time (hours)dependent: y: gallons

DOMAIN: 0 ≤ x ≤ 20

RANGE: 0 ≤ y ≤ 1200

4) Write the NEXT-NOW statements for the following:

a) 8, - 10, - 28

c)

b) 25, 20, 16

A hot tub contains 1200 gallons and is being drained. Every hour the volume decreases by 60 gallons.

NEXT = NOW – 18, Starting at 8

NEXT = NOW *4/5, Starting at 25

NEXT = NOW – 60, Starting at 1200

4) Write the NEXT-NOW statements for the following:

d)

-1 1 2

1

2

3

4

5

6

x

y

(0, 6)

(1, 4)

r = 4/6 = 2/3

NEXT = NOW *2/3, Starting at 6

4) Write the NEXT-NOW statements for the following:

e)

x 2 3 4

y 4 10 16

f) The value of a house increases 4.3 % a year. In 2010, it was $ 200,000.

61

6

23

410

m

4 = 6(2) + b4 = 12 + b- 8 = by = 6 x – 8

NEXT = NOW + 6, Starting at - 8

NEXT = NOW * 1.043, Starting at 200,000

5) Find the rate of change of the following:

b)

a) (5, 6) to (8, 9)

-1 1 2

1

2

3

4

5

6

x

y

(0, 6)

(1, 4)

13

3

58

69

r

3

2

6

4r

5) Find the rate of change of the following:

d)

c) y = 3 x + 9 from [1, 4].

y = 2x from [3, 5].

y1 = 3(1) + 9 = 3 + 9 = 12

(1, 12)

y4 = 3(4) + 9 = 12 + 9 = 21

(4, 21)

33

9

14

1221

r

y3 = 23 = 8

(3, 8)

y5 = 25 = 32

(5, 32)

122

24

35

832

r

5) Find the rate of change of the following:

f)

e)

x2 + 4 x + 2 from [1, 5].

x 2 3 4

y 4 10 166

1

6

23

410

r

y1 = 1 + 4(1) + 2 = 1 + 4 + 2 = 7

(1, 7)

y5 = 25 + 4(5) + 2 = 25 + 20 + 2 = 47

(5, 47)

104

40

15

747

r

6)

a) How is f(x – 3) + 2 shifted from f(x)?

b) How is 2x+1 shifted from 2x + 1?

c) How is (x + 3)2 + 1 shifted from (x – 2)2 +1?

d) Which equation represents 3x+1 + 2 shifted 3 left and 4 down?

right 3, up 2

left 1, down 1

left 5

f(x) = 3x+4 – 2

7)

Lucy wants to invest $ 3000 into a financial plan. Two financial institutions offer the following choices: A: y = 3000 + 150 x B: 3000(1.015)x

a) Describe each plan in words.

b) Which plan is better for Lucy after 1 year? after 10 years?

A: earns $ 150 per year, starting at $ 3000B: earns 1.5 % interest per year, starting at $ 3000

A: y = 3000 + 150(10) = 3000 + 1500 = 4500B: y = 3000(1.015)10 = 3,481.62

A

after 30 years?A: y = 3000 + 150(30) = 3000 + 4500 = 7500B: y = 3000(1.015)30 = 4,689.24

A

8)A f(x) and g(x) are graphed. Graph f(x) + g(x) on interval [-1, 3].

-1 1 2 3 4

-5

-4

-3

-2

-1

1

2

3

x

y

f(x) = x2 – 2 x – 1 g(x) = x –

1

f(x) + g(x) = x2 – x – 2

8)B h(x) = 2; i(x) = x2 – 2. Graphh(x) + i(x) from [0, 3].

-1 1 2 3 4

-5-4-3-2-1

123456789

x

y

f(x) + g(x) = 2 + x2 – 2 = x2

9) Suppose that average price of gasoline is given by:

Year 2000 2001 2003 2005 2007

Price $ 1.30 $ 1.47 $ 1.48 $ 1.82 $ 2.27

a) Write an equation that best fits this situation. (Let x = 0 for 2000) b) What is the average price increase per year? c) Describe the correlation.

d) What was the predicted cost of gasoline in 2008? e) Determine the residuals and determine which year had the highest residual?

y = .13 x + 1.26 $

0.13

r = .95

positive

$ 2.28

Year Residual

2000 .04

2001 .08

2003 .16

2005 .08

2007 .11

2003 had the highest

residual,

10) The table shows the Richter scale that measures earthquake intensity.

Richter No.

4 5 6 7 8

Increase in

Magnitude

1000 10000 100000 1000000 10000000

a) What type of equation is the best model (linear, quadratic, or exponential)?

b) Write the prediction equation. Specify what x and y are.

c) Predict the increase of magnitude for a 7.2 earthquake.

d) Predict the Richter scale number for an increase of 5000000 in magnitude.

exponential

y = .1(10)x

x: Richter number y: increase in magnitude

1,584,893.2

7.7

11) Find (or estimate) the coefficient of correlation:

a) (0, 2), (1, 8), (3, 11), (4, 19)

b)

r = .96

r = .93

11) Find (or estimate) the coefficient of correlation:

c)

r = - .97

12)f(x) = 3 x + 2. The RANGE is {8, 11, 14}. Find the DOMAIN.

3 x + 2 = 83 x = 6x = 2

3 x + 2 = 113 x =

9x = 3

3 x + 2 = 143 x =

12x = 4

DOMAIN:

{2, 3, 4}

13)Mr. Thompson is making a 30 point quiz that only contains True/False equations worth 3 points and Multiple Choice questions that are worth 5 points. What are the possible members of the domain? (True/False are the x-values.)x = number of True/Falsey = number of Multiple Choice3 x + 5 y =

30DOMAIN: {0, 5, 10}

14)f(x) = 2(1/2)x+2 g(x) = 2(1/2)x + 3 How is f(x) different from g(x)?f(x) is g(x) shifted to the left 2

and down 3.

15)The function h(x) = 2(1/2)x is replaced with h(x) + k. What is k?

k = 3

16)Fred and Gail’s grandmother decided to give them money monthly in a different manner. Both started with $ 20. Fred’s grandmother added $ 75 each month. Gail’s grandmother doubled it every month. At the end of which month will they have the same amount of money?Fred: y = 75 x + 20Gail: y = 20(2)x

At the end of the 4th month, they will both have $ 320.

17)What is the average rate of change?

Year 2000 2001 2003 2005 2007

Price $ 1.30 $ 1.47 $ 1.48 $ 1.82 $ 2.27

$ 0.13

18)Alberto turned the faucet on in a bathtub and then measured the depth of the water at 1-minute intervals. His data is displayed in the table below:Time (min) 1 3 6 9 12 15

Depth(cm) 3 7 12 20 26 33

a) Find the linear equation of best fit. b) Identify and interpret the slope. c) Identify and interpret the y-intercept.

d) Predict the water depth after 16 minutes.

e) Predict when the water will be 38 cm.

f) What percent of the residuals was higher than 1 cm?

y = 2.15 x + .32Slope is 2.15

Centimeter increase per minutey-intercept is .32 which is the beginning amt. of

water34.78 cm.

17.5 minutes

1/6 = 16.6 %

19)A scientist recorded the growth g (in inches) of pine trees and the amount of rainfall r (in inches) they received in their first year.

R (in.) 0 3 5 12 17 22 34 35 45

G (in.) 1 4 6 9.5 10.8

10.9

6 5.3 1

a) According to the correlation coefficients, which model best fits the data? (linear, exponential, or quadratic)

b) Write the equation that best fits the data.

c) According to your equation, find the height of a pine tree with 28 inches of rainfall in its first year.

quadraticy = .019 x2 + .797 x + 1.942

9.498 in.

20)The table below shows the population of two towns.

a) Which town is growing linearly? How much is it increasing by?

b) Which town is growing exponentially? How much is it increasing by?

c) What is the rate of growth for each town from 2010-2013?

Year Population of Springtown

Population of Summertown

2010 20,000 20,000

2011 21,900 25,000

2012 24,100 31,250

2013 26,000 39,063

Springtown

2020

Summertown

2000

2000

20)The table below shows the population of two towns.Year Population of

SpringtownPopulation of Summertown

2010 20,000 20,000

2011 21,900 25,000

2012 24,100 31,250

2013 26,000 39,063

d) Write the NEXT-NOW equations for both towns.

e) Write an equation that demonstrates the growth of both towns.

f) Predict the population in 2015 for both towns.

Springtown: NEXT = NOW + 2020; Start at 20,000Summertown: NEXT = NOW * 1.25; Start at

20,000Springtown: y = 2020 x + 19970Summertown: y = 19999.95(1.25)x

Springtown: 30,070

Summertown: 61,036

21)The table below shows the total cost at a restaurant for different amounts of people.

Number of People

1 2 3 4

Total Cost of Bill $ 15 $ 22.50

$ 30 $ 37.50

Which function below represents the cost at a restaurant for “n” amount of people?A) C(n) = 15 n B) C(n) = 15 + n

C) C(n) = 7.50 n + 1

D) C(n) = 7.50(n – 1) + 15

y = 7.5 x + 7.5

22)The balance in an account at the end of the year can be represented by the formula NEXT = (1.075)NOW. The account was opened 6 years ago. The balance at the end of 3 years was $ 2,034.56. What was the balance at the end of 6 years?

A) $ 31,400 B) $ 29,200

C) $ 25,300 D) $ 21,900

23)The amount of people in a waiting room can be represented by the formulaNEXT = NOW + 2. At the beginning of the day, 6 people are waiting. How many people are waiting 5 hours later?A) 10 people B) 12 people

C) 14 people D) 16 people

24)The water filling up in a bathtub is modeled by the equation V = 4 t + 3 where V is the volume (gallons) and t is the time (minutes) after 8:00 PM. What is the meaning of the y-intercept in the problem?

A) The average rate that the bathtub is filling up.B) The amount of water in the tub once it is filled.C) The amount of water at 8:00 PM.

D) The amount of gallons that the bathtub is increasing by each minute.

25)The water filling up in a bathtub is modeled by the equation V = 4 t + 3 where V is the volume (gallons) and t is the time (minutes) after 8:00 PM. What is the meaning of the slope in the problem?

A) The average rate that the bathtub is filling up.B) The amount of water in the tub once it is filled.C) The amount of water at 8:00 PM.

D) The amount of gallons that the bathtub is increasing by each minute.

26)

A) There is a strong negative relationship.B) There is a weak negative relationship.C) There is a strong positive relationship.D) There is a weak positive relationship.

Which of the following statements best describes the correlation?

27)

A) A B) B C) C D) D

Which point has the highest residual?