# Functions Functions A Relation is a set by wuzhengqin

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```									                                            Functions
A Relation is a set of ordered pairs of numbers.

A Function is a relation in which domain element has a unique range element.

Domain: all the x-values in the relation.

Range: all the y-values in the relation.

Vertical Line Test: If a vertical line cross the graph no more than once, everywhere, the graph
represents a function.

State the domain and the range for the relation, then determine if the relation is a function.

{ (2, 1), (3, -4), (5, -6), (-3, 8), (-6, 5) }
Domain:
Range:
Function:

{ (-3, -4), (5, 4), (-3, 8), (6, 6), (5, 4) }
Domain:
Range:
Function:

{ (2, 1), (3, 1), (5, 1), (-3, -1) }
Domain:
Range:
Function:
Use the vertical line test to determine if each graph represents a function. State its domain and
range.

Domain:                                                 Domain:

Range:                                                  Range:

Function: yes                                           Function?
All lines that are
not vertical
are functions.

Domain:                                              Domain:

Range:                                               Range:

Function?                                            Function?
Domain:       Domain:

Range:        Range:

Function:     Function?

Domain:     Domain:

Range:      Range:

Function?   Function?
Let g(x) = x2 + 1 Find:

g(-4)                     g(5)             g(0)

g( t )                    g( 2a )   g( 3 ) – 6
Function Notation: F(x) = 3x – 7
The function name is F, and this function is in terms of x.

To evaluate the function at -3, we write F(-3)
F(-3) = 3(-3) – 7
-9 – 7
-16

Let f (x ) 5  2 x Find:

f (1)                                               f (0 )

f (a 2 )                                            f (a ) 2
F(x) = 2    F(x) = 3

F(2) =      F(-2) =

F(x) = -3   F(x) = 3

F(1) =      F(3) =

```
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