Start with a numerical representation of a function $f$:
$x\ $ \t $-4$ \t $-3$ \t $-2$ \t $-1$ \t $0$ \t $1$ \t $2$ \t $3$ \t $4$
\\ $f(x)$ \t $%4$ \t $%5$ \t $%6$ \t $%7$ \t $%8$ \t $%9$ \t $%10$ \t $%11$ \t $%12$
If we use the values of $f(x)$ in the table as values of $y$ and then plot the resulting points $(x,y)$, we get the following graph, called the graph of the function $f$,
where we have connected the successive points by line segments. Click on any point on the graph to see its coordinates.
Now pretend that someone had deleted the table and all you had was the graph above. You could then recover all the values in the table by "reading them off" the graph: For instance, to find $f(-2)$, click on the $x$-axis where $x = -2$, then follow the arrows vertically to the graph and then horizontally to read off the corresponing $y$-coordinate: $y = %6$. Thus,
$f(-2) = %6. \qquad$
We can also use the graph as drawn to estimate values of $f(x)$ when $x$ is between two values on the table, for instance,
$f(2.5) = %13. \qquad$
(Click on the $x$-axis at $x = 2.5$ to check this.) This value of $f(x)$ is called an interpolated
value, as we inferred it from the graph even though it was not specified originally. Another way of thinking about it is that the graph sepcifies a function whose domain is the whole closed interval $[-4, 4]$.
Some for you: