Algebra / English

Algebra Basics: What Are Functions? - Math Antics

mathantics · YouTube · 11:34

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Define a function by one output per input and connect tables, graphs and function notation.

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Chapters

1:30Domain and range 4:30One output for every input 9:00Function notation

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The domain is the set of allowed inputs. The range is the set of outputs actually attained and may be smaller than the stated output set or codomain.

The relation y²=x permits both $y=2$ and $y=-2$ when $x=4$ , so it is not a single-valued function y of x without a branch restriction. By contrast $y=2x$ gives one output per input.

In $f(x)$ , f names the function and the parentheses indicate its input; this is not multiplication of f by x. Turning input-output pairs into plotted points connects the table and graph descriptions.

Knowledge cards

Domain and range

The domain is the set of allowed inputs. The range is the set of outputs actually attained and may be smaller than the stated output set or codomain.

One output for every input

The relation y²=x permits both $y=2$ and $y=-2$ when $x=4$ , so it is not a single-valued function y of x without a branch restriction. By contrast $y=2x$ gives one output per input.

Function notation

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Functions ExplanationAt 1:30
Why this connection?
The domain is the set of allowed inputs. The range is the set of outputs actually attained and may be smaller than the stated output set or codomain. The relation y²=x permits both $y=2$ and $y=-2$ when $x=4$ , so it is not a single-valued function y of x without a branch restriction. By contrast $y=2x$ gives one output per input. In $f(x)$ , f names the function and the parentheses indicate its input; this is not multiplication of f by x. Turning input-output pairs into plotted points connects the table and graph descriptions.