Functions & Relations

Relation Any set of input that has an output

Frayer Model Definition Examples Relation Linear Non-Linear

Frayer Model Definition Examples Relation Linear Non-Linear

Frayer Model A set containing pairs of numbers Relation Definition Examples A set containing pairs of numbers Relation Linear Non-Linear

Frayer Model {(2,1), (1,3), (0,4)} A set containing pairs of numbers 2 Definition Examples {(2,1), (1,3), (0,4)} A set containing pairs of numbers 2 1 1 3 4 x y 2 1 1 3 4 Relation Linear Non-Linear

Frayer Model {(2,1), (1,3), (0,4)} A set containing pairs of numbers 2 Definition Examples {(2,1), (1,3), (0,4)} A set containing pairs of numbers 2 1 1 3 4 x y 2 1 1 3 4 Relation Linear Non-Linear

Frayer Model {(2,1), (1,3), (0,4)} A set containing pairs of numbers 2 Definition Examples {(2,1), (1,3), (0,4)} A set containing pairs of numbers 2 1 1 3 4 x y 2 1 1 3 4 Relation Linear Non-Linear

Domain x – coordinates Input Independent variable

Range y – coordinates Output Dependent variable

When listing the domain and range, Put in order from least to greatest Only list repeats once

Example Write the domain and range for the following relation. {(2, 6), (-4,-8), (-3,6), (0,-4)}

You Try 1) Write the domain and range for the following relation. {(-5,2), (3,-1), (3,2), (1,7)}

You Try What are the domain and range?

Function A relation such that every single input has exactly ONE output Each element from the domain is paired with one and only one element from the range

How do we describe FUNCTIONS ?

Frayer Model Definition Examples a relation in which each input (x value) is paired with exactly one output (y value). Function Linear Non-Linear

Frayer Model {(1,2), (2,4), (3,6)} 1 2 3 2 4 6 x y 1 2 3 2 4 6 Definition Examples {(1,2), (2,4), (3,6)} a relation in which each input (x value) is paired with exactly one output (y value). 1 2 3 2 4 6 x y 1 2 3 2 4 6 Function Linear Non-Linear

Frayer Model {(1,2), (2,4), (3,6)} 1 2 3 2 4 6 x y 1 2 3 2 4 6 Definition Examples {(1,2), (2,4), (3,6)} a relation in which each input (x value) is paired with exactly one output (y value). 1 2 3 2 4 6 x y 1 2 3 2 4 6 Function Linear Non-Linear

Frayer Model {(1,2), (2,4), (3,6)} 1 2 3 2 4 6 x y 1 2 3 2 4 6 Definition Examples {(1,2), (2,4), (3,6)} a relation in which each input (x value) is paired with exactly one output (y value). 1 2 3 2 4 6 x y 1 2 3 2 4 6 Function Linear Non-Linear

Very Important!!! All functions are relations but not all relations are functions.

How do I know it’s a function? Look at the input and output table – Each input must have exactly one output. (Domains CANNOT repeat!!!) Look at the Graph – The Vertical Line test: NO vertical line can pass through two or more points on the graph

Is this relation a function? {(1,3), (2,3), (3,3)} Yes No Answer Now

Are these relations functions? (1, 2), (3, 4), (1, 5), (2, 6) (6, 9), (7, 10), (8, 11), (8, –11) (–1, –5), (–2, –7), (0, 3), (1, –5) 4. (2, 4), (3, 5), (2, -4), (3, –5)

Are these relations functions? x 1 2 3 4 y 5 6 7 1. 2. 3. x 2 4 5 Y 1 3 x 6 5 4 3 Y -1 -2 -3 -4

Are these relations functions? 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

Vertical Line Test (pencil test) If any vertical line passes through more than one point of the graph, then that relation is not a function. Are these functions? FUNCTION! FUNCTION! NOPE!

Vertical Line Test FUNCTION! NO! NO WAY! FUNCTION!

Is this a graph of a function? Yes No Answer Now

An Equation is not a Function if… the “y” variable is raised to an EVEN power; x = any number; x = 5 and x = -9 these are vertical lines.

Are these functions? y = x 2 x + y 4 = 5 y = x + 3 y + 6 = x 3 x = 3 Yes No, y is raised to an even power! No, because the line is vertical!

How do you know if a relation is a function? Tell Your Neighbor How do you know if a relation is a function?

Wednesday: Warm Up Is this relation a function? Explain how you know. {(3,4), (0,7), (3, -4), (2,5)} Vocab Warm-Up Page 465

Tuesday Warm Up  

Thursday Warm-Up Create a table with two columns labeled “Relation and Function” and “Relation Only” Give examples of each in the following forms: ordered pairs table mapping graph

Test Your Neighbor Make a list of coordinate pairs. Ask your neighbor if the relation is a function.

Error Analysis-Functions Success Starter for 1/9/17 Error Analysis-Functions When asked whether the relation {(-4,16), (-2,4), (0,0), (2,4)} is a function, Zion stated that the relation is not a function because 4 appears twice. What error did Zion make? How would you explain to the student why this relation is a function? Also, write the domain and range.

Lesson Review Write the definition of the following vocabulary terms: Domain Range Relation Function

Make a mapping diagram of a relation Make a mapping diagram of a relation. Ask your neighbor if the relation is a function.

Does the graph represent y as a function of x? Explain.

Warm Up