The Evil Testing Serpent likes to test your ability to move back and forth
between a function and its graph. Like so:
The graph of f (x) is shown above. If f (z) = 6, what is ?
What we need to understand, looking at the graph, is that if f (z) = 6, that
means that our output, or y, is equal to 6. Can we tell which input (x)
corresponds to the output (y) of 6? Sure, it’s the only x point we’re told: 1. So
.
Notice how each x-coordinate has only one corresponding y-coordinate. This
fact makes our relation a function. A relation is only properly called a function if
each x has only one y value. On the other hand, when a y value corresponds to
more than one x value (such as a horizontal line), the relation is still a function.
Confused? Think of it this way: In math class, each student (x) has only one
score (y), but the same score (y) can be achieved by many different students (x).
It is far easier to tell if a relation is also a function by looking at its graph. If you
can draw a vertical line through any part of the graph, and it only touches one