holt algebra 2 1-6 relations and functions identify the domain and range of relations and functions....
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Holt Algebra 2
1-6 Relations and Functions
Identify the domain and range of relations and functions.
Determine whether a relation is a function.
Objectives
Vocabulary Words
Relation and FunctionVertical Line TestDomain and Range
Holt Algebra 2
1-6 Relations and Functions
A relation is a pairing of input values with output values. It can be shown as a set of ordered pairs (x,y), where x is an input and y is an output.
The set of input (x) values for a relation is called the domain, and the set of output (y) values is called the range.
Holt Algebra 2
1-6 Relations and Functions
A
B
C
2
Domain Range
Mapping Diagram
Set of Ordered Pairs
{(2, A), (2, B), (2, C)}
(x, y) (domain, range)
Holt Algebra 2
1-6 Relations and Functions
Example 1: Identifying Domain and Range
Give the domain and range for this relation:
{(100, 5), (120, 5), (140, 6), (160, 6), (180, 12)}
{(100,5), (120,5), (140,6), (160,6), (180,12)}.
The set of x-coordinates.
The set of y-coordinates.
Domain: {100, 120, 140, 160, 180}
Range: {5, 6, 12}
List the set of ordered pairs:
Holt Algebra 2
1-6 Relations and Functions
Example 2
Give the domain and range for the relation shown in the graph.
Domain: {–2, –1, 0, 1, 2, 3}
Range: {–3, –2, –1, 0, 1, 2}
List the set of ordered pairs:
{(–2, 2), (–1, 1), (0, 0), (1, –1), (2, –2), (3, –3)}
The set of x-coordinates.
The set of y-coordinates.
Holt Algebra 2
1-6 Relations and Functions
Not a function: The relationship from number to letter is not a function because the domain value 2 is mapped to the range values A, B, and C.
Function: The relationship from letter to number is a function because each letter in the domain is mapped to only one number in the range.
Both functions and non-functions are relations!
Holt Algebra 2
1-6 Relations and Functions
Holt Algebra 2
1-6 Relations and Functions
Use the vertical-line test to determine whether the relation is a function. If not, identify two points a vertical line would pass through.
Example 3A: Using the Vertical-Line Test
This is a function. Any vertical line would pass through only one point on the graph.
Holt Algebra 2
1-6 Relations and Functions
Example 3B Using the Vertical-Line Test
Use the vertical-line test to determine whether the relation is a function. If not, identify two points a vertical line would pass through.
This is a function. Any vertical line would pass through only one point on the graph.
Holt Algebra 2
1-6 Relations and Functions
This is not a function. A vertical line at x = 1 would pass through (1, 1) and (1, –2).
Use the vertical-line test to determine whether the relation is a function. If not, identify two points a vertical line would pass through.
Example 3C: Using the Vertical-Line Test
Holt Algebra 2
1-6 Relations and Functions
Example 4A: Is this relation a function?
From graph or ordered pairs:
{(–2, 2), (–1, 1), (0, 0), (1, –1), (2, –2), (3, –3)}
Function: The relationship is a function if each member of the domain is mapped to only one number in the range.
Holt Algebra 2
1-6 Relations and Functions
Example 4B: Is this relation a function?
{(100,5), (120,5), (140,6), (160,6), (180,12)}.
Domain: {100, 120, 140, 160, 180}
Range: {5, 6, 12}
Identify the domain and range:
Function: The relationship is a function if each member of the domain is mapped to only one number in the range.
Holt Algebra 2
1-6 Relations and Functions
Example 4C: Is this relation a function?
A.
B. Names in a classroom and grades
There is only one price for each shoe size. The relation from shoe sizes to price makes is a function.
C. (Reverse B…) from class grades, find student name.
Holt Algebra 2
1-6 Relations and Functions
This is not a function. A vertical line at x = 1 would pass through (1, 2) and (1, –2).
Example 5A: Is this relation a function?
Use the vertical-line test to determine whether the relation is a function. If not, identify two points a vertical line would pass through.
Holt Algebra 2
1-6 Relations and Functions
Example 5B: Is this relation a function?
Use the vertical-line test to determine whether the relation is a function. If not, identify two points a vertical line would pass through.
not a function