In this lesson we will answer the following question:
What is a Funtion?
A Function is a special type of mapping.
What is a Mapping?
Recall that a mapping shows how
each member of the domain
is paired with each member of the range
A function is a special mapping in which
each element in the domain
must map to ONLY one element in the range.
Is the relation a function?
Is this relation a function?
Yes! each element of x maps to only one element of y. Note: it does not matter that an element in y is used twice!
The Vertical Line Test
If no vertical line intersects the graph in more than one point, then the graph represents a function.
This graph passes the vertical line test It represents a function.
This graph does not pass the vertical line test and does not represent a function.
Can you determine if the relations below are functions?
No, See how the x coordinate 2 maps to two y-coordinates, (3 and -4)
Yes, it is a function. This graph passes the Vertical Line test
Yes, it is a function. Each x-coordinate maps to only 1 y-coordinate
To determine if a relation is a function:
Check to see if each x-coordinate maps to exactly one y-coordinate