The graph in
Figure 14 does
not make
a function of
Two ordered pairs on that graph are
and
so an input value is used twice with different output values.
The graph in
Figure 15 does
not make
a function of
There are many ordered pairs with the same input value but different output values. For example,
and
The graph in
Figure 16 does make
a function of
It appears that no matter what
-value you choose on the
-axis, there is exactly one
-value paired up with it on the graph.
The graph in
Figure 17 does make
a function of
but we should discuss. The hollow dots on the line indicate that the line goes right up to that point, but never reaches it. We say there is a “hole” in the graph at these places. For two of these holes, there is a separate ordered pair immediately above or below the hole. The graph has the ordered pair
It
also has ordered pairs like
but it does not have
Overall, there is no
-value that is used twice with different
-values, so this graph does make
a function of
The graph in
Figure 15 does
not make
a function of
There are many ordered pairs with the same input value but different output values. For example,
and
all use
The graph in
Figure 15 does
not make
a function of
There are many ordered pairs with the same input value but different output values. For example at
there is both a positive and a negative associated
-value. It’s hard to say exactly what these
-values are, but we don’t have to.