Functions

• Definition:– For every input, there is only one output– For every “x” there is only one “y”

• How to tell if a function is represent…– Do the input (x) values repeat?• If No…Function!!!• If Yes…Not a Function

– Does the graph pass the vertical line test?

Domain and Range

Algebra 1

Domain

• The Domain is all of the “x” values of a function– The Domain represents all values that are being

inputted into a function

• Horizontal Values

Range

• The Range is all of the “y” values of a function– The Range represents all values that are being

outputted into a function

• Vertical Values

Find the Domain and RangeX 3 4 6 -4

Y 11 14 17 20

Domain: { -4, 3, 4, 6 }

Range: { 11, 14, 17, 20 }

Find the Domain and RangeX -10 -8 -6 -8

Y 3 4 5 6

Domain: N/A

Range: N/A

Find the Domain and RangeX 5 15 25 35

Y 5 5 5 5

Domain: { 5, 15 , 25, 35}

Range: { 5 }

Writing Domain and Range from a Continuous Graph

• Because it is impossible to write every value of x and y on a continuous graph, we use inequalities to help

• Inequalities help us make an interval

Domain : { lowest x value < x < highest x value }Range: { lowest y value < y < highest y value }

Find the Domain and Range

Domain: { -3 < x < 8 }

Range: { -3 < y < 5 }

Find the Domain and Range

Find the Domain and RangeDomain: { -5 < x < 9 }

Range: { -5 < y < 5 }

Find the Domain and Range

Domain: { x > 1}

Range: { y > 0}

Find the Domain and Range

Range: { y < 7}

Find the Domain and Range

Range: { y > -5 }

Find the Domain and Range

Range: { y < 0 }

Find the Domain and RangeDomain: { -6 < x < 5}

Range: { -7 < y < 5}