I can determine whether a relation is a function 2.5A: What is a function? I can determine whether a relation is a function

f x y x y Recall… input output Definition of a function: Each ____is paired with only one ____ x y input x is called the _________ y is called the _________ Each input gives its own output output x y f Function Machine

Example 1 When each element in the domain (x) is paired When we graph f(x) = x + 2, is it a function? How can we tell? x y -2 -1 1 2 1 2 When each element in the domain (x) is paired with one element in the range (y) 3 4

Vertical Line Test (VLT) This is a function – a vertical line only hits the graph once This is a NOT a function – a vertical line hits the graph more than once

Does this graph pass the VLT?

Does this graph pass the VLT?

Does this graph pass the VLT?

YES! YES! Mappings: Example 2 -1 1 2 2 3 4 5 -1 1 2 2 x y -1 2 3 1 4 5 3 1 4 5 -1 1 2 2 3 4 5 Is this a function? YES! x y -1 2 1 -1 1 2 Is this a function? 2 YES!

NO! It is a function if each ‘x’ gets mapped to ONLY ONE ‘y’ -1 2 2 3 3 4 5 -1 2 2 3 4 5 Is this a function? NO!

A. B. Are you a master? (1, 3) (2, 5) (1, -8) Which of the following are functions? A. B. (1, 3) (2, 5) (1, -8)

C. D. Are you a master? 3 6 4 8 Which of the following are relations? x y 3 6 4 7 8 3 6 8 4