3 1 Domain and Range Using Interval Notation

3. 1 Domain and Range Using Interval Notation

Alphabetical Order is our FRIEND!! • domain • x • input • horizontal • range • y • output • vertical • d comes before r • x come before y • i comes before o • h comes before v

Interval Notation [ and ] are used with closed dots to denote inclusion Like a fence you can touch or lean against [ ] for ( and ) are used with open dots and arrows to denote exclusion It is still a fence, but it is an electric fence – DON’T touch it! ( ) for ∞ is the symbol for infinity

Mapping Diagrams Given the following relation: {(1, -2), (-2, 0), (-1, 2), (1, 3)}. Make a Mapping Diagram of the function. Then determine if it is a function. Domain -2 -1 1 Range -2 0 2 3 Function? No. It is not a function. The input 1 has 2 outputs, thus is fails the 1: 1 test.

Graphing Given the following relation: {(1, -2), (-2, 0), (-1, 2), (1, 3)}. Make a Mapping Diagram of the function. Then determine if it is a function.

1: 1 • Each input can have only one output, hence the ratio of 1: 1. • 1 input has 1 output. • Each function test checks for this 1: 1 nature. • Ordered pairs: • If an x repeats with a different y that input has more than one output. 1: 2 is not 1: 1. • Mapping Diagrams: • If an element of the Domain has more than arrow leaving it that input has more than one output. • Graphing: • The vertical line test (aka the pencil test), checks for a single input having multiple outputs. • Thus all tests are actually the same test.