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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