Definitions
What is a relation in mathematics?
A set of ordered pairs.
Is {(1, 2), (3, 4), (1, 5)} a function?
No, because input 1 maps to two different outputs.
List two mapping types
Any two of
One-to-many one-to-one
many-to-many
many-to-one
What test do we use on a graph to check if it’s a function?
The vertical line test.
What is a function?
A relation in which each input has exactly one output.
True or False: A vertical line on a graph always represents a function.
False.
What does it mean if two inputs map to the same output?
It can still be a function.
What does it mean if a vertical line touches the graph more than once?
It’s not a function.
What is the domain of a relation?
The set of all input (x) values.
Is the mapping diagram where 2 arrows come from the same input a function?
No, because one input has multiple outputs.
Which two types of mapping represent non-functions
one-to-many
many-to-many
Draw a graph that fails the vertical line test.
Student draws a "c" or circle or similar
Q: What is the range of a function?
The set of all output (y) values.
Can a function have repeated output values?
Yes, as long as each input has only one output.
Create a mapping diagram that represents a function.
Each input with one arrow to one output
Is the graph of y=x2 a function?
Yes.