Algebra 2: Lesson 2.4 Functions

Functions and Non-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 and Range Concepts

• 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.

Specific Examples of Domain and Range

• 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.

Additional Domain and Range Examples

• 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.