domain
the first element (x-value) of a relation or function; also known as the input
function
a function is a relation such that for each first element (x-value, input) there exists one and only one (unique) second element. Another way to say this is that none of the ordered pairs have a repetitive x-value. That is, every first element (x-value, i
input
the input is the x-value of a relation or function
output
the output is the y-value of the relation or function
range
the second element (y-value) of a relation or function; also known as the output.
relation
a relation is any set of numbers that are able to be graphed on a coordinate (x, y) plane. A relation can be a function, but is not always a function
Relations and Functions: Definitions
A person can only be in one place at one time. At any one moment, a person only measures one thing, they can't be both one hundred fifty pounds and 90 pounds. That isn't possible. A student's overall class grade can be passing or failing. It can't be both
DEFINITIONS
You may recall from your study of two-variable equations that the graphs of those equations are in a two-dimensional plane. Each point on the graph has an ordered pair that describes its location. Each ordered pair "solves" the equation. You can think of
Example 1:
A = {(6, 2), (2, 6), (4, 1), (4, 0)}
Set A is a relation because it is a set of ordered-pair numbers. Set A is finite with four members. Although the set of ordered pairs is considered to be a relation, it is not considered a function since it has x-value
Example 2:
B = {(x, y) | x + y = 5}
Set B is a relation; it is also an infinite set because it does not contain a definite set of x and y values. From the infinite set, we conclude that the domain and range of the linear function is all real numbers.
Remember:
Set A
Example 3:
C = {(2, 5), (6, 1), (8, 2), (9, 5), (4, 10)}
Set C is a function because each first element is listed only once.
Domain: (2, 6, 8, 9, 4) Range: (5, 1, 2, 10)
Example 4:
D = {(2, 6), (5, 1), (2, 7), (8, 3)}
Set D is not a function because first element 2 has two different values for second elements, 6 and 7. However, set D is a relation because any set of ordered pairs is a relation.
Example 5:
E = {(x, y) | x - y = 8}
Set E is a function because for any value chosen for x, you will get a single value for y. Notice that Set E uses the rule method for designating the set. This linear function has a domain and range of all real numbers since it is
Example 6:
Determine if the relation is a function. If the relation is a function, name the domain and range.
{(-1, 7) (3, 0) (1, 4) (-5, 9)}
This relation is a function because as you can see, the x-values are not repetitive. In case you are wondering why the x-val
*
The domain and range can be listed in the order the numbers are given or can be rearranged numerically, lowest number to highest number. It is not necessary to list repeated numbers.
1. domain
2. function
3. input
4. output
5. range
6. relation
4. the y-value of a function.
6. any set of ordered pairs (x, y) that are able to be graphed on a coordinate plane.
2. a relation in which every input value has exactly one output value.
3. the x-value of a function.
5. the second element of a relation or
Select either relation (if the set is a relation but not a function), function (if the set is both a relation and a function), or neither (if the set is not a relation).
A = {(1, 2) (2, 2) (3, 2) (4, 2)}
function
Select either relation (if the set is a relation but not a function), function (if the set is both a relation and a function), or neither (if the set is not a relation).
input -1 0 -1 -8 9
output 0 1 2 4 8
relation
If the relation is a function, list the domain and range. If the relation is not a function, choose "not a function".
C = {(9, 1) (8, -3) (7, 5) (-5, 3)}
Domain: {9, 8, 7, -5} Range: {1, -3, 5, 3}
Select either relation (if the set is a relation but not a function), function (if the set is both a relation and a function), or neither (if the set is not a relation).
F = {(x, y ) | x + y = 10}
relation
Select the domain and range of F.
F = {(x, y ) | x + y = 10}.
Domain: {10} Range: {10}
Which of the following statements best represents the relationship between a relation and a function.
A function is always a relation but a relation is not always a function.
1. the domain set of C = {( 2, 5), (2, 6), (2, 7)}
2. the range set of E = {(3, 3), (4, 4), (5, 5), (6, 6)}
3. the range and domain of F = {(x, y ) | x + y =10}
4. the range and domain of P = {(x, y) | y = 3}
1. {2}
2. {3, 4, 5, 6}
3. domain = range = {all real numbers}
4. domain = {all real numbers}: range = {y: y = 3}