DOMAIN AND RANGEDOMAIN AND RANGE

Vertical line test

A test use to check if the relation is a function. If the vertical line passes through more than one point of

the graph, then it’s NOT a function

yes No

Domain and range

Domain Range

Domain is the set of the first coordinates

Range is the set of the second coordinates

Function: a relation that assigns to each value in the domain exactly one value in the range.

Example:

Find the domain and range of this function:

Determine if the relation is a FUNCTION

Domain Range

The relationship is NOT a function

The relationship is a function

Domain Range

Warm-upWarm-upUse the Vertical Line Test to determine the function:

Function Not a Function Function

Determine if the relations are a Function by mapping

Function Function

Finding the Domain and range

Domain:

Range:

All real numbers

y: y ≥ 1

y, such that y is ≥ to 1

Your Turn!Graph and find the domain and range of the following

function

y = x2 - 1 domain: {-1,0,1,2}

x y = x2 - 1 (x, y)

–1 y = (-1)2 - 1 = 0 (–1, 0)

0 y = (0)2 - 1 = -1 (0, -1)

1 y = (1)2 - 1 = 0 (1, 0)

2 y = (2)2 - 1 = 3 (2, 3)

Domain:

Range:

All real numbers

y: y ≥ -1

Domain and Range

Domain: all real numbers

Range: {y | y≥ -3}

Domain and Range

Domain: all real numbers

Range: {y | y ≤ 3}

Classwork