12.2 Functions and Graphs

F(X) = x+4 where the domain is {-2,-1,0,1,2,3}

To determine if an equation is a function…

Create a (x, y) table

Is y = x² a function?

Is x = y2 a function?

No, because x = 9 is equal to both 3 and –3.

Is y = |x| a function?

Is x = |y| a function?

No, because x = 7 is equal to both 7 and –7.

YES

To determine if a graph is a function…

Perform the Vertical Line Test

Is this a graph of a function?

Vertical

Line

Test

Is this a graph of a function?

Is this a graph of a function?

Is this a graph of a function?

Is this a graph of a function?

Is this a graph of a function?

Domain of a Function

• X values have to make the value a real number

• Watch for 0 in the denominator

• Watch for – under the square root (set radicand )0

Find the domain of

Domain is {x | x 4}

1( )

4g x

x

Find the domain of

Domain is {x | x -5}

( ) 5h x x 5 0x

5x

Find the domain of

Domain is all real numbers

2( ) 7f x x

Find the domain of

Domain is {x | x 4}

3( )

4f x

x

Find the domain of

Domain is {x | x 7}

( ) 7g x x

7 0x 7x

Graph and State Domain and Range

• Domain is horizontal coverage

• Range is vertical coverage

Find the domain of f(x) = 2x + 1

Domain is all real numbers

Find the range of f(x) = 2x + 1

Range is all real numbers

Find the range of

( ) 2g x x x y024-2-4-6

Range is { y | y 0 }

x y0 22 44 6-2 0-4 2-6 4

x y024-2-4-6

Find the range of

( ) 1f x x x y0 -12 14 3-2 1-4 3-6 5

Range is { y | y -1 }

AssignmentPage 545

(2-10 even and 11-31all)