Notes from a PPT: Functions vs. Relations / Domain & Range

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Notes from a PPT: Functions vs. Relations / Domain & Range Coordinate Algebra Agenda: Notes from a PPT: Functions vs. Relations / Domain & Range Learning Target: Students can define a relation and explain the difference between a relation and a function. Students can determine the domain and range of relations and functions. Standard: MCC9-12.F.IF.1 and 2

Functions vs. Relations

Relation A relation is simply a set of ordered pairs. The set of all first values (x- values) is the domain. The set of all second values (y-values) is the range.

Function A relation where EACH input has exactly ONE output Each element from the domain is paired with one and only one element from the range

Domain x – coordinates Independent variable Input

Range y – coordinates Dependent variable Output

How do I know it’s a function? Look at the input and output table – Each input must have exactly one output. Look at the Graph – The Vertical Line test: NO vertical line can pass through two or more points on the graph

function Example 1: {(3, 2), (4, 3), (5, 4), (6, 5)} Is the following relation a function? Example 1: {(3, 2), (4, 3), (5, 4), (6, 5)} function

Is the following relation a function? Example 2: function

Is the following relation a function? Example 3: relation

function Is the following relation a function? Example 4: ( x, y) = (student’s name, shirt color) function

Is the following relation a function? Example 5: Red Graph relation

function Is the following relation a function? Jacob Angela Nick Honda Example 6 Jacob Angela Nick Greg Tayla Trevor Honda Toyota Ford function

function A person’s cell phone number versus their name. Is the following relation a function? Example 7 A person’s cell phone number versus their name. function

Only list repeated values once Put in order from least to greatest Domain and Range Only list repeated values once Put in order from least to greatest

What are the Domain and Range? {1, 2, 3, 4, 5, 6} {1, 3, 6, 10, 15, 21}

What are the Domain and Range? {0, 1, 2, 3, 4} {1, 2, 4, 8, 16}

What are the Domain and Range? All Reals All Reals

What are the Domain and Range? x ≥ -1 All Reals

Functions Practice worksheet Homework Functions Practice worksheet