1.6 Relations and Functions

Appetizers . . . Can a student have more than one telephone number? Can a student have more than one height? Can a phone number belong to more than one person?

Some Vocabulary so we all speak the same language . . . relation: a pairing of input values with output values, such as an ordered pair. For any (x, y), x is the input and y is the output. domain: set of input values for a relation. range: set of output values for a relation.

Table Graph Mapping Diagram 123456 9 13 15 12 10 Ordered Pairs {(1, 9), (2, 13), (3, 15), (4, 15), (5, 12), (6, 10)} domain (input) range (output)

Function or not a function? That is the question! function: there is only one output for each input, so each element of the domain is mapped to exactly one element in the range. Huh? No repeats for x. Repeats on y are OK. A B C A B C 2 2 NOT a function Function {2, A), (2, B), (2, C)} 2 is used more than once {A, 2), (B, 2), (C, 2)} 2 is used more than once

Function or not a function? That is the question! Press Function or NOT a Function, then explain. -2 -1 1 2 5 6 7 8 X Function NOT a Function

Function or not a function? That is the question! Press Function or NOT a Function, then explain. -2 -1 1 2 3 4 5 X Function NOT a Function

Function or not a function? That is the question! Press Function or NOT a Function, then explain. Input Value –2 –1 1 2 Output Value –8 8 X Function NOT a Function

Function or not a function? That is the question! Press Function or NOT a Function, then explain. Input Value 1 2 Output Value –4 –2 4 X Function NOT a Function

Function or not a function? That is the question! Press Function or NOT a Function, then explain. {(1, 0), (2, –1), (3, 0), (3, – 1), (4, 0)} X Function NOT a Function

Function or not a function? That is the question! Press Function or NOT a Function, then explain. {(1, 0), (2, –1), (3, 0), (4, –1)} X Function NOT a Function

What about graphs? Vertical line test (VLT): If any vertical line passes through more than one point on the graph of a relation the relation is not a function. Function

VLT, cont. Not a Function

VLT, cont. Function Not a Function

VLT, cont. Function Not a Function

VLT, cont. Function Not a Function

VLT, cont. Function Not a Function

VLT, cont. Function Not a Function

VLT, cont. Function Not a Function

Finding Domain and Range from a Graph

Helicopter taking off, hovering briefly, then landing.

Speeding baseball being caught by an outfielder.

Helicopter taking off, hovering briefly, then landing.

1.7 Function Notation

y is now f(x) function function notation Find y when x=-3; or evaluate the function when x=-3

Any letter goes! function function notation