9/8/2015 1 Relations and Functions Unit 3-3 Sec. 3.1.

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Relations and Functions

Unit 3-3

Sec. 3.1

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Definitions: Relations – a set of ordered pairs

Domain – the set of all possible input values of a relation or function. (x-values, input, independent variables).

Range – the set of all possible output values of a relation or function. (y-values, output, dependent variables).

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Identifying the Domain & Range

{(100 , 5), (120, 5 ), (140, 6 ), (160, 6), (180, 12)}

Example 1:Example 1:

Domain:

Range:

List Domain and Range in increasing order!!!List Domain and Range in increasing order!!!

{5, 6, 12}

{100, 120, 140, 160, 180}

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Identify the Domain & Range

Example 2:Example 2:

Domain:

Range:

{3, 5, 7}

{-1, 0, 9}

The arrow leaves the input values (x) and points at the output values (y).

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Example 3:Domain: {1, 2, 3}

Range: {2}123

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Identify the Domain & Range

Example 4:Example 4:List the x-values for Domain and the y-values for Range

Domain:

Range:

{ }-2,-1, 0, 1, 2, 3

{ }-3,-2, -1, 0, 1, 2

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Definition

Function – a relation in which every input is paired with exactly one output.

- For every x, there is one y

- 2 inputs can have the same output, but an input cannot have 2 outputs.

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Function or Not a Function?Function – a relation in which every input is paired with exactly one output.

Function? Function?NO! YES!

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Function?

{(100 , 5), (120, 5 ), (140, 6 ), (160, 6), (180, 12)}

Example 1:Example 1:

YES!

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Function?

Example 2:Example 2:

NO!

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Vertical Line Test

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Function?

YES! NO!

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Your Turn

YES! NO!

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Function Notation

If x is the independent variable and y is the dependent variable, then the function notation for y is f(x), read “f of x” where f names the function.

Ex. y = 2x

f(x) = 2x

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Evaluating Functions

Evaluate f(-2).

( ) 7 2f x x

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Evaluating Functions

Evaluate f(1) and f(a)

2( ) 4f x x x

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Your Turn

Evaluate f(3).

( ) 2 1f x x

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Evaluating Functions on a Graph

f(0) = f(1/2) = f(-2) = 3

0 4

Assignment

P. 229#15-25 odd, and 27 a, b, c

DUE: TOMORROW!

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