Domain and Range

TEKSIdentify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete.

TEXTBOOK PGS 35 - 37

Domain: the set of all INPUTS in a relation.All POSSIBLE x-values! List each value only once and in order from least to greatest.

RANGE:

The set of all OUTPUTS in a relation.

All POSSIBLE y-values! List each value only once and in order from least to greatest.

EXAMPLE 1

yx

1

2

3

4

3

5

7

9

Domain: ____________

Range: _____________

{ 1, 2, 3, 4 }

{ 3, 5, 7, 9 }

All x-values from smallest to biggest

All y –values from smallest to biggest

EXAMPLE 2

{(-3,3),(-1,2),(1,1),(1,3),(3,-2),(4,-2)}

D =

R =

{-3, -1, 1, 3, 4}

{-2, 1, 2, 3}

EXAMPLE 3The chart below is called a mapping. It maps each input to its output(s). Find the domain and range of the mapping.

DOMAIN:

RANGE:3-25

104

23-2-8

INPUT OUTPUT

2,3,4,5,10

8, 2,2,3

EXAMPLE 4

Find the range of the given equation when the domain is {-5, 0,

5}:y = 3x2 - 1

Range: {-1, 74}

Finding Domain and Range from a Graph

There are two different kinds of graphs—discrete (no line) and continuous (line). You will write the domain and range differently depending on which type of graph it is.

DISCRETE DATA:

All of the above examples contain _________, or _________ date. We know its __________because the domain and range come from ordered pairs or points on a graph. When the data is _________, we only include the __________________ or coordinate values in the domain and range. _____________ the points on a graph when the data is discrete.

discrete

discrete

discrete

countable

listed numbers

DO NOT connect

EXAMPLE of a DISCRETE GRAPH

D =

R =

{-3, -2, 0, 2}{-1, 0, 3, 4}(-3, 0)

(-2, 3)

(0, 4)

(2, -1)

***CONTINUOUS DATA***

When you have ____________ data, connect the points on the graph. ____________ data __________ all of the numbers and fractions between the line’s end points. The domain will begin at the farthest left point of the graph and go the farthest right point. The range will start at the lowest point of the graph and move to the highest.

D:

R:

______________ x _____________

______________ y _____________

Farthest left x-value Farthest right x-value

lowest y-value highest y-value

continuous

continuous includes

EXAMPLE of a CONTINUOUS Graph

D=

R =

6 x 7

6.75 y 5.2

Domain: 0 to 16 hoursRange: $0 to $112

Identify the independent and dependent variables. Find reasonable domain and range values for this situation.

Maria earns $7 per hour for baby-sitting after school and on Saturday. She works no more than 16 hours a week.

Independent: The number of hours she worksDependent: The amount Maria earns

Reason: The amount Maria earns depends on the number of hours she works in a week.

D:

R:

LET’S PRACTICE!

X

4

5

5

6

-1

y

-1

2

3

6

1

1,4,5,6

1,1,2,3,6

{(2,3),(3,0),(5,2),(-1,-2),(4,1)}

DOMAIN:

RANGE:

1,2,3,4,5

2,0,1,2,3

Continuous…

D:

R:

6 x 5

4 y 4

Discrete…

D:

R:

6, 2, 1,3,5

6, 4, 1,5

Domain: 0 to 12 gallons of gasRange: 0 to 300 miles

Tara’s car travels about 25 miles on one gallon of gas. She has between 10 and 12 gallons of gas in the tank.

Independent: Number of gallons of gasDependent: Distance traveled

Reason: The distance Tara travels depends on how much gas is in her car.

Identify the independent and dependent variables. Find reasonable domain and range values for this situation.