In this type of diagram, the left circle represents the x values, and the right circle represents the y values.
Remember that an ordered pair has the form:
[tex](x,y)[/tex]
So to find the set of ordered pairs represented by the arrows, we need to start in the left circle (that would be the x value) and follow the arrow to the right circle (that would be the y value).
Let's start with the first arrow, shown in blue for reference:
The ordered pair represented by this arrow is:
[tex](5,12)[/tex]
We continue with the second arrow:
The ordered pair represented by this arrow is:
[tex](16,23)[/tex]
We continue with the third arrow:
The ordered pair represented by this arrow is:
[tex](0,10)[/tex]
Next, the fourth arrow:
The ordered pair that this arrow represents is:
[tex](0,0)[/tex]
At this point, not that we have two different y values (10 and 0) for the same x value (0), this will be useful to define if the relation is a function.
We continue with the last arrow:
The ordered pair is:
[tex](-14,-2)[/tex]
The set of ordered pairs:
(5,12), (16,23), (0,10), (0,0), (-14,-2)
To define id the relation is a function, we use the following rule:
• A set of ordered pairs will not be a function if you have two different values of y for the same value of x.
Since that is the case for the relation in the diagram (remember that we have the ordered pairs (0,10) and (0,0)--> different y values for the same x value), the relation is not a function.
Answer:
The set of ordered pairs:
(5,12), (16,23), (0,10), (0,0), (-14,-2)
Not a function.
