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Domain & RangeDomain & Range
A function is a set of ordered A function is a set of ordered pairs of numbers (x, y) such pairs of numbers (x, y) such that no x –values are repeated. that no x –values are repeated.
What are the domain and range What are the domain and range of a function?of a function?
The domain and range of a The domain and range of a function are sets that describe function are sets that describe those ordered pairs.those ordered pairs.
DefinitionDefinition ExampleExample
{(3, 6), (2, 8), {(3, 6), (2, 8), (5, 3)}(5, 3)}
DomaDomainin
All the x-All the x-coordinates in the coordinates in the function's ordered function's ordered pairspairs
{ 3, 2, 5}{ 3, 2, 5}
RangRangee
All the y-All the y-coordinates in the coordinates in the function's ordered function's ordered pairspairs
{ 6, 8, 3}{ 6, 8, 3}
The domain is the set of all the The domain is the set of all the values of the independent values of the independent variable, the x-coordinatevariable, the x-coordinate
The range is the set of all the The range is the set of all the values of the dependent values of the dependent variable, the y-coordinate.variable, the y-coordinate.
Identify the domain and range Identify the domain and range of the function below.of the function below.
{ 2, 7), (4, 11), (6, 15), (8, 19)}{ 2, 7), (4, 11), (6, 15), (8, 19)}
The domain is { 2, 4, 6, 8}The domain is { 2, 4, 6, 8}
The range is { 7, 11, 15, 19}The range is { 7, 11, 15, 19}
What is the domain of this What is the domain of this function?function?
What is the range of this What is the range of this function?function?
Domain is 0 ≤ x ≤ 4
Range is 1 ≤ y ≤ 5
The graph shows the path of a golf The graph shows the path of a golf ballball
What is the range of this function?
F 0 < y < 100
G 0 ≤ y ≤ 100
H 0 ≤ x ≤ 5
J 0 ≤ x ≤ 5
What is the domain of this What is the domain of this
function?function?
A -1 ≤ x ≤ 5
B -1 ≤ x ≤ 9
C 2 ≤ x ≤ 5
D 0 ≤ y ≤ 9
What is the domain of the What is the domain of the function shown on the graph?function shown on the graph?
A -2 < y ≤ 2
B -4 ≤ x ≤ 6
C -4 < y ≤ 2
D -2 < x ≤ 6
The Vertical Line The Vertical Line TestTest
The vertical line test is used The vertical line test is used to determine if a graph is a to determine if a graph is a
function.function.
If a vertical line passes through a graph more than once, the graph is not the graph
of a function. Hint:
Pass a pencil across the graph held vertically to
represent a vertical line.The pencil crosses the
graph more than once. This is not a function
because there are two y-values for the same x-
value.