• function

• coordinate system• y-axis• origin• x-axis• ordered pair• x-coordinate• y-coordinate

• Interpret graphs of functions.

• independent variable• dependent variable• relation• domain• range• discrete function• continuous function

• Draw graphs of functions.

A.1 The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. (A) Describe independent and dependent quantities in functional relationships. A.2 The student uses the properties and attributes of functions. (B) Identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete. (C) Interpret situations in terms of given graphs or creates situations that fit given graphs. Also addresses TEKS A.1(D).

MEDICINE Name the ordered pair at point E and explain what it represents.

Point E is at 6 along the x-axis and about 100 along the y-axis.

Answer: The ordered pair is (6, 100). This represents about 100% normal blood flow 6 days after the injury.

Identify Coordinates

A. A

B. B

C. C

D. D

A. (4, 97); This represents 97% normal blood flow 4 days after the injury.

B. (6, 100); This represents 100% normal blood flow 6 days after the injury.

C. (0, 50); This represents 50% normal blood flow 0 days after the injury.

D. (2, 75); This represents 75% normal blood flow 2 days after the injury.

Name the ordered pair at point D and explain what it represents.

0% 0%0%0%

Independent and Dependent Variables

A. ENERGY In warm climates, the average amount of electricity used rises as the daily average temperature increases, and falls as the daily average temperature decreases. Identify the independent and the dependent variables for this function.

Answer: Temperature is the independent variable as it is unaffected by the amount of electricity used. Electricity usage is the dependent variable as it is affected by the temperature.

Independent and Dependent Variables

B. The number of calories you burn increases as the number of minutes that you walk increases. Identify the independent and the dependent variables for this function.

Answer: The time is the independent variable. The number of calories burned is the dependent variable as it is affected by the time

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. The number of new members is the independent variable. The dues is the dependent variable.

B. Membership dues is the independent variable. Number of new members is the dependent variable.

C. x is the independent. y is the dependent.

D. Both are independent.

A. In a particular club, as membership dues increase, the number of new members decreases. Identify the independent and dependent variable in this function.

1. A

2. B

3. C

4. D

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A B C D

A. The length of the side is independent, and the the area of the square is dependent.

B. The area is independent, and the side length is dependent.

C. Both variables are independent.D. Both are dependent.

B. The area of a square increases as the length of a side increases. Identify the independent and dependent variable in this function.

Analyze Graphs

The graph represents the temperature in Ms. Ling’s classroom on a winter school day. Describe what is happening in the graph.

Sample answer: The temperature is low until the heat is turned on. Then the temperature fluctuates up and down because of the thermostat. Finally the temperature drops when the heat is turned off.

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. Macy is doing bobs.

B. Macy’s speed increases as she crosses the length of the pool, but then decreases to zero when she turns around at the end of each lap.

C. Macy is swimming at a constant speed.

D. Macy’s speed continues to decrease.

The graph below represents Macy’s speed as she swims laps in a pool. Describe what is happening in the graph.

A. SCHOOL CAFETERIA There are three lunch periods at a school. During the first period, 352 students eat. During the second period, 304 students eat. During the third period, 391 students eat. Make a table showing the number of students for each of the three lunch periods.

Answer:

Draw Graphs

B. Write the data as a set of ordered pairs. Then draw the graph.

The ordered pairs can be determined from the table. The period is the independent variable and the number of students is the dependent variable.

Answer: The ordered pairs are (1, 352), (2, 304), and (3, 391).

Draw Graphs

Answer:

Draw Graphs

A. A

B. B

C. C

D. D

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A. At a car dealership, a salesman worked for three days. On the first day he sold 5 cars. On the second day he sold 3 cars. On the third he sold 8 cars. Make a table showing the number of cars sold for each day.

A.

B.

C.

D.

A. A

B. B

C. C

D. D

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B. Write the data as a set of ordered pairs. Then draw the graph.A. (1, 5), (2, 3), (3, 8) B. (1, 2), (3, 5), (3, 8)

C. (1, 3), (2, 3), (3, 3) D. (1, 3), (2, 2), (3, 5)

Domain and Range

A. TUTORING Mr. Ohms tutors students. He works at most 120 hours for $4 per hour. Identify a domain and range for this situation.

The domain is the number of students he can tutor. Up to 120 students can be tutored. Therefore, a reasonable domain would be values from 0 to 120 students. The range is the total charged from $0 to 120 × $4 or $480. Thus, a reasonable range is $0 to $480.

Answer: Domain: 0–120; Range: $0–$480

B. Draw a graph that shows the relationship.

Graph the ordered pairs (0, 0) and (120, 480). Since any number of students up to 120 students will be tutored, connect the two points with a line to include those points.`

Domain and Range

Answer:

C. State whether the function is discrete or continuous. Explain.

Domain and Range

Answer: Since the points are connected with a line, the function is continuous.

A. A

B. B

C. C

D. D

0% 0%0%0%

A. Domain: $0 to $6250Range: 0 – 250

B. Domain: 0 – 250 Range: $0 to $6250

C. Domain: 0 – 25 Range: 0 – 25

D. Domain: 0 – 25 Range: 0 – 250

A. Prom tickets are on sale at a high school for $25 per person. The banquet room where the prom is being held can hold up to 250 people. Identify a reasonable domain and range for this situation.

A. A

B. B

C. C

D. D

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B. Draw a graph that shows the relationship between the number of persons attending the prom and total admission price.A. B.

C. D.

A. A

B. B

C. C

D. D

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A. Discrete

B. Continuous

C. Both discrete and continuous

D. Neither discrete nor continuous

C. State whether the function is discrete or continuous.

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