MATH 109

Exam 1 Review

Jeopardy

Data FunctionsPicturing Functions

Straight As An Arrow

Potpourri

100 100 100 100 100

200 200 200 200 200

300 300 300 300 300

400 400 400 400 400

500 500 500 500 500

Data 100

• Suppose that the mean starting salary of your graduating class (6000 people) is $50,000 a year. One of your fellow classmates is a newly drafted basketball player star and makes a whopping $30 million dollars a year, an obvious outlier.

• What would be the mean starting salary for the graduating class if we threw out this outlier? Round your answer to the nearest thousand dollars.

• Answer: $45,000

Data 200

• A news article about the local housing market states that the mean cost of a home is $240,000 while the median cost is about $225,000.

• What conclusions can you draw about these to statistics and which do you think is more representative of the typical cost of a home?

• Answer: The median tells us that 50% of homes cost at or above $225,000 and 50% of homes cost at or below $225,000. The fact that the mean is higher than the median suggests that the mean is probably somewhat inflated due to high outliers in the data. Because of this, the median is probably gives a better representation of the typical cost of a home.

Data 300

• You are taking MATH 150 at Fairview Community College. You are told by the instructor that the median grade in the class is 65%. What information does this give you about how you will do in the class?

• Answer: Fifty percent of the class got a 65% or better in the course. We can also say that fifty percent of the class got a 65% or under in the course. Since we don’t have a histogram to show the distribution of grades, it is difficult to determine just how spread out the grades in the course really are.

Data 400

• Table below shows undergraduate enrollment at the U of A for several years:

• Find the average rate of change for undergraduate enrollment from 2000 to 2004. Include units.

• Answer: enrollment grows on average by 491 students per year.

year Enrollment2000 264042001 275322002 282782003 284822004 28368

Data 500

• The data below shows the number of points scored by the U of A football team for the last two seasons:

• 24 31 24 0 21 16 21 29 5214 20 16 3 28 3 10 720 10 27 24 37 14

• Construct a histogram of the frequencies with bins of size 10.

U of A Points Scored

6 68

20

1

02468

10

10 20 30 40 50 60

Points

# o

f ti

mes

Functions 100

• Which of the following express y as a function of x?

x 1 -3 2 0y 4 3 4 1

x 1 0 2 0y 4 3 4 1

x 2 -3 2 0y 4 3 4 1

042 xy 04 xyy 0442 xy

Functions 200

• Which of the following functions has a domain of [1,∞) ?

x

xf

1

1

1

1

xxg

1

1

x

xh 1 xxp

Functions 300

• State the domain AND range for the graph of f(x) shown below:

• Domain: [2,7] ; Range: [0,9]

Functions 400

• Given the function:

• Find the domain of f

• Answer: [0,2) U (2,∞)

2

4

x

xxf

Functions 500

• Determine the RANGE of the function

• Range: [1,∞)

21

1

xxf

Picturing Functions 500

• You fly from Phoenix, Arizona to Orlando, Florida with a connecting flight in Dallas Ft Worth, Texas. The flight has to circle in Orlando, Florida before being allowed to land. Sketch a graph of your distance from Dallas Ft Worth as a function of time. Assume that Dallas Ft Worth is closer to Phoenix.

Picturing Functions 400

• The number of people who own an IPhone increases slowly at first but then grows rapidly until the market is saturated with IPhone users. Sketch a graph of the number of IPhone users as a function of time.

Picturing Functions 300

• A turkey is taken out of the refrigerator and placed into a 400 degree oven to cook. At various times the cook opens the oven to check on the temperature of the turkey. Sketch the turkey’s temperature as a function of time.

Picturing Functions 200

• The temperature of a hot cup of coffee placed into a room whose ambient temperature is 70 degrees. Sketch a graph of the coffee’s temperature as a function of time.

Picturing Functions 100

• The price of a stock declines slowly with time but then declines even more rapidly later. Sketch the price of the stock as a function of time.

Potpourri 400

• The graphs of two perpendicular lines are shown below:

• Find the equation of the line whose graph is represented by the dashed line

• Find the coordinates of the point P. Round your answer to three decimal places.

(1.274, 4.603)

6583 xy

Potpourri 300

• Which of the following tables represent a linear function?

x y x y x y10 50 -3 -0.27 -4 1620 25 -2 -0.08 -1 8.530 12.5 -1 -0.01 0 640 6.25 0 0 2 150 3.125 1 0.01 8 -14

Potpourri 200

• Sketch the graph of a function whose domain is the set of all real numbers and whose range is y < 0.

Potpourri 100

• When a large airliner approaches an airport, it begins its descent from about 100 miles away & takes 20 minutes to descend from an altitude of 36,000 feet.

• Express the airliner’s altitude as a linear function of time.

• Find and interpret the slope and intercepts. y-int (0, 36000 ft) (altitude before making descent) , x-int (20 min, 0) (time it takes to descend to an altitude of 0 ft)

tA 180036000

Potpourri 500

• An 8 foot ladder is leaning up against a wall (see below). Depending on the distance between the ladder’s base and the wall, d, the ladder will reach a certain height, h up the wall.

• Express h as a function of d. • Determine a reasonable domain for the function you found.

Domain: [0,8]

264 ddh

Straight As An Arrow 400

• In a college meal plan you pay a membership fee; then all your meals are at a fixed price per meal. Suppose 30 meals cost $152.50 and 60 meals cost $250.

• Write a formula for the cost of a meal plan, C, in terms of the number of meals, n.

• Find the cost for 50 meals.

• How many meals can you buy for $300?

About 75 meals

5525.3 nnC

50.217$50 C

Straight As An Arrow 500

• A restaurant owner graphed his daily profits in terms of the number of meals served and found that the relationship was linear. When 105 meals were served the restaurant’s profits were $150. During another day, 90 meals served resulted in a $100 profit.

• Express profits as a linear function of the number of meals served.

• What does the slope tell you?Each meal served increases profits by $3.33 (or every 3 meals served means profits go up by $10)

• What does the vertical intercept tell you?When zero meals are served restaurant loses $200. This is probably the daily overhead of running the restaurant.

• Find and interpret the horizontal intercept? (60,0) ; At 60 meals the restaurant breaks even.

200310 mmP

Straight As An Arrow 300

• At a price of $2.30 per gallon, the average weekly demand by consumers for gasoline is 42 gallons. When price is $2.35 per gallon, the weekly demand is 39 gallons.

• Find a formula for the weekly demand as a function of the price per gallon. Assume that demand is linear.

• Find an interpret and intercepts of your formula.

vertical intercept: (0,180) means when the selling price is $0 per gallon, the weekly demand is 120 gallons.

horizontal intercept: (3,0) means when the selling price is $3 per gallon, the weekly demand is zero.

ppQ 60180

Straight As An Arrow 200

• Residents of the town of a certain town are connected to the municipal water supply. They are billed a fixed amount yearly plus a charge for each cubic foot of water used. A household using 1000 cubic feet of water was billed $90, while one using 1600 cubic feet was billed $120.

• What is the charge per cubic foot?

$0.05 per cubic foot of water used

• What is the fixed amount residents are billed yearly?

$40 annual fee

Straight As An Arrow 100

• The balance B on a car loan after n monthly payments is given by the function B = f(n) = 10800-300n.

• Rewrite the above function strictly in terms of units.

• Find and interpret the zero(s) of this function.

(36,0) ; after 36 monthly payments, the balance on your loan is zero.

• Determine an appropriate domain and range for this function.

Domain: [0,36] ; Range: [0,10800]

payment$$ payment$