Algebra 2: Lesson 2.4 Functions

A table can represent a function if each input (X value) corresponds to exactly one output (Y value).
Mapping defines a function similarly; it must pair each input with one unique output.
A table can be identified as not a function if any input is linked to multiple outputs.
Graphs can illustrate functions when any vertical line intersects the graph at most once.
A mapping is not a function if an input yields multiple outputs.
Relations can be classified as functions or not based on whether they meet the unique output criteria for each input.

Domain refers to the complete set of possible input values (X values).
Range is the complete set of possible output values (Y values).
The domain of a given function may be specified as {3, 4}, indicating only these values are valid inputs.
The range can consist of a single value, such as {9}, meaning all outputs correspond to that number.
Multiple pairs can share the same output; for example, the pair (3,9) appears multiple times without changing the output value.

The domain example {1, 2, -3, 10, -8} shows valid X values derived from given pairs like {(1, 0), (2, 2), (-3, 5), (10, 6), (-8, 0)}.
A range example such as {0, 2, 5, 6} highlights multiple outputs that can be sourced from various input pairs.
The domain {0, 1, 2, 3, 4, 5, 6, 7} captures a continuous set of input options.
The defined range of {0, 1.75, 2.5, 3.25, 4, 5.75, 6.5, 7.25} indicates various unique output values from corresponding input values.
Definitions clarify the distinction: the domain is all X values, while the range encompasses all Y values.

Examples such as domain { -1, 0, 1 } and range { -3, 7, 10 } illustrate specific sets of values.
Similarly, another domain example { -1, 0, 2, 4 } presents valid inputs, while range {6, 16, 11, 21} gives corresponding outputs.