Download Function Definition

Function: Definition
A function is a correspondence between two sets governed
by some rule(s) such that each member of the first set
corresponds to exactly one member of the second set.
The first set is called the domain of the function.
The second set is called the range of the function.
In this course the members of each set are real numbers.
For now, x will represent a real number from the domain
and y or f (x) will represent a real number from the range.
The independent variable, x, denotes a member of the
domain and the dependent variable, y, denotes a member
of the range. We say, "y is a function of x".
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Function: Mapping Diagram Representation
A function may be represented using a set of ordered
pairs (x, y), a table of values, an equation, a graph, and a
mapping diagram.
Here is an example of a function represented in part, by a
mapping diagram.
17
5
0
2
-2
-4
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Slide 2
Function: Mapping Diagram Representation
Here, the left oval represents in part, the domain.
The right oval represents in part, the range.
17
5
0
-2
2
-4
The rules that govern the correspondence between the
two sets are: 1. Multiply the domain value by three.
2. Add two to the result.
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Slide 3
Function: Ordered Pairs, Table Representations
17
5
0
2
-2
-4
Here is the same function represented in part, by a set
of ordered pairs: { (- 2, - 4), (0, 2), (5, 17) }.
x y
Here is the same function represented
-2 -4
in part, by a table of values:
0 2
5 17
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Slide 4
Function: Equation, Graph Representations
17
5
0
2
-2
-4
Here is the same function represented by an equation:
y = 3x + 2 or f (x) = 3x + 2.
Here is the same function
represented by a graph
(orange line pictured).
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Slide 5
Function
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