function: definition a function is a correspondence from a first set, called the domain, to a second...
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Function: Definition
• A function is a correspondence from a first set, called the domain, to a second set, called the range, such that each element in the domain corresponds to exactly one element in the range.
• Domain elements are called inputs.
• Range elements are called outputs.
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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".
Function: Definition
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.
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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 by a mapping diagram.
5 17
0 2
- 2 - 4
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The rules that govern the correspondence between the two sets are:
1. Multiply the domain value by three.
2. Add two to the result.
Function: Mapping Diagram Representation
Here, the left oval represents the domain. The right oval represents the range.
5 17
0 2
- 2 - 4
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Here is the same function represented by a set of ordered pairs:
{ (- 2, - 4), (0, 2), (5, 17) }.
Function: Ordered Pairs
5 17
0 2
- 2 - 4
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Function: Table Representations
5 17
0 2
- 2 - 4
Here is the same function represented by a table of values:
x y
- 2 - 40 2 5 17
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Let’s say that the mapping is just a partial representation of infinitely many ordered pairs. Then here is the same function represented by an equation:
y = 3x + 2 or f (x) = 3x + 2.
Function: Equation
5 17
0 2
- 2 - 4
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Function: Graph Representations
5 17
0 2
- 2 - 4
Here is the same function represented by a graph (orange line pictured).
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Function