[Algebra II] 1.1

Function

A relation that assigns exactly one output for each input, often represented as f(x).

Domain

The set of all possible input values (x) for a given function, where each input corresponds to an output.

Range

The set of all possible output values (f(x)) for a given function, derived from the domain.

Codomain

The set of all potential output values for a function, which includes the range but may also contain additional values not produced by the function.

One-to-one function

Each y value (output) has only one x value (input)

Onto Function

Range is the same as Codomain

Horizontal Line Test

If a horizontal line intersects a graphed function more than once then the function is not one-to-one, if it intersets once it is one-to-one

All Real Numbers

-Infinity —> +infinity

Continous Function

Graphed curve is not broken / no gap

Discrete Function

Graphed dots are not connected

Neither Continous nor Discrete function

Graphed line / curve is broken

What is the domain and range of discrete functions

The dots’ x and y values respectively

Set-Builder Notation

{X | X > 0}

Interval Notation

(-oo, 0)

Filled in circle (Include)

Greater / less than or equal to

Empty circle (Exclude)

Greater / Less than

[

Used when include

(

Used when exclude

{

Used for set builder notation

∈ R

Is an Element of all Real Numbers

All real numbers (Set-Builder Notation)

{X | -oo < X < oo}

How to combine Set-Builder

or

How to combine interval notation

U (union)