• coordinate system

• x- and y-axes

• origin

• ordered pair

• x- and y-coordinates

A plane, also called a coordinate grid or coordinate system, in which a horizontal number line and a vertical number line intersect at their zero points.

• Relation--A set of ordered pairs

• Domain--The set of the first numbers or abscissas of the ordered pairs in a relation.

• Range--The set of second numbers in the ordered pairs of a relation.

• independent variable--The variable in a function whose value is subject to choice.

• dependent variable--The variable in a relation whose value depends on the value of the independent variable.

Representations of a Relation

A. Express the relation {(4, 3), (–2, –1), (2, –4), (0, –4)} as a table, a graph, and a mapping.

Table List the x-coordinates in the first column and the corresponding y-coordinates in the second column.

Representations of a Relation

Graph Graph each ordered pair on a coordinate plane.

Representations of a Relation

Mapping List the x-values in the domain and the y-values in the range. Draw an arrow from the x-value to the corresponding y-value.

4

–2

2

0

3

–1

–4

Domain Range

Representations of a Relation

B. Determine the domain and range for the relation {(4, 3), (–2, –1), (2, –4), (0, –4)}.

Answer: The domain for this relation is {4, –2, 2, 0}. The range is {3, –1, –4}.

A. A

B. B

C. C

D. D

A. Express the relation {(3, –2), (4, 6), (5, 2), (–1, 3)} as a mapping.

A. C.

B. D.

A. A

B. B

C. C

D. D

B. Determine the domain and range of the relation {(3, –2), (4, 6), (5, 2), (–1, 3)}.

A. D = {–1, 3, 4, 5}; R = {–2, 2, 3, 6}

B. D = {–2, 2, 3, 6}; R = {–1, 3, 4, 5}

C. D = {–1, 3}; R = {–2, 2}

D. D = {4}; R = {4}

• The distance, d, traveled by a wheel is given by the equation d = 7r, where r is the number of rotations that the wheel undergoes. Which of the following is true?– d is dependent on r.– Both d and r are independent variables.– r is dependent on d.– Both d and r are dependent variables.

• Albert's monthly income can be expressed by the equation: i = 10h + 12, where i is his income in dollars, and h is the number of hours that he worked. Which of the following is true?– h is dependent on i.– Both i and h are independent variables.– i is dependent on h.– Both i and h are dependent variables

• If exposing plants to low temperatures results in changes in the colors of the leaves, and the two variables are linearly related, which of the following is true?– Both leaf color and temperature are

dependent variables.– Temperature is an independent variable.– Both leaf color and temperature are

independent variables.– Leaf color is an independent variable.

Independent and Dependent Variables

A. CLIMATE 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.

A. A

B. B

C. C

D. 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.

A. A

B. B

C. C

D. 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 increases after 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.

A. A

B. B

C. C

D. 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.

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