domain and range النطاق والمدى
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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.