BELL RINGER 12-8-11EXPLORE REVIEWPut your EXPLORE DATA and you Test Booklet on your

desk.

1. Plant A is 12 inches tall and grows at a rate of 1.5 inches per week. Plant B is 6 inches tall and grows at a rate of 2.0 inches per week. The 2 plants will be the same height at the end of how many weeks.

2. What is the mean of the 6 numbers below: 32, 36, 50, 52, 52, 66

3. Nathan misspelled 1 out of every 4 words on a spelling test. How many words did he get correct.

4. #30 in Explore Booklet

1-6 RELATIONSObjectives:By the end of this class period, with an

85% accuracy, students will be able to:

Represent relations in multiple ways Identify dependent and independent

variables in real-life situations Describe what is happening in graphs

of relations

RELATIONS A relation is a set of ordered pairs. It can be

represented in several waysWith a mappingWith a table In a graphAs an equation

A mapping shows how each element in the domain is paired with each element in the range. Draw 2 ovals and arrows mapping the x-

values to the y-values. Example:

PracticeA. 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.

3 WAYS TO REPRESENT A RELATION

Representations of a Relation

{(4, 3), (–2, –1), (2, –4), (0, –4)}B. Graph each ordered pair on a coordinate plane on the graph paper provided (top right).

Representations of a Relation

{(4, 3), (–2, –1), (2, –4), (0, –4)}

C. 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

Domainx

Rangey

DOMAIN AND RANGEDomain (D) is the set of all x-values (the 1st

number in the ordered pair)Range (R) is the set of all y-values (the 2nd

number in the ordered pair)

Representations of a Relation

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

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

Individual PracticeA.Express the relation {(3, –2), (4, 6), (5, 2), (–

1, 3)} as a mapping.

A. C.

B. D.

An independent variable is the value of the variable that determines the output. x is the independent variable. It can stand alone.

A dependent variable is the value that is dependent on the independent variable. y is the dependent variable. It depends on the other variable.

Example: 1

Your height increases as you get older. What are the independent and dependent variables for this relation?

A person’s age and height.

Which variable depends on the other?

Your height depends on how old you are (age).

Height is the dependent variable.

Age is the independent variable.

Independent and Dependent Variables

EXAMPLE 22. 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 relation.

What are the 2 variables?Temperature and electricity usage.Electricity usage depends on the temperature.

Temperature is the independent variable since it is unaffected by the amount of electricity used.

Electricity usage is the dependent variable sinceit is affected by the temperature.

EXAMPLE 3B. 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 relation.

What are the 2 variables?The number of minutes you walk (time) and the number of calories burned.Number of calories burned depends on the number of minutes walked (time).

The time is the independent variable.The number of calories burned is the dependent variable since it is affected by the time.

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

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

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

D.Both variables 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 relation.

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 variables are dependent.

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

ANALYZE GRAPHS

A relation can be graphed without a scale on either axis. These graphs can be interpreted by analyzing their shape.

See p. 42 Example 3 See graphY depends on x. The distance depends on the

time.Distance – dependent and time - independent

As the time increases the distance increases until the graph becomes a horizontal line. Time increases but the distance remains the same. At this section, she stopped. Then she continued to ride her bike.

Analyze Graphs

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

(y) Temperature depends on the (x) time.Temperature – dependent and time independent

Sample: The temperature increases after the heat is turned on. Then the temperature goes up and down because of the thermostat. Finally, the temperature drops when the heat is turned off.

Example:

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

EXIT SLIP

1. P. 65 #63Express the relation shown in each

table, mapping or graph as a set of ordered pairs.

2. p. 43 #7

HOMEWORK

p. 43 10-14 even, 20-26 all

Bring Graph Paper daily.