Question

=WORTH 50 POINT=

1) Draw an example of a graph that is a function.

2) Draw an example of a graph that is not a function.

Label each graph and explain why each graph is a function or not.

Answer 1

The graph of f(x) in this example is the graph of y = x2 - 3. It is easy to generate points on the graph. Choose a value for the first coordinate, then evaluate f at that number to find the second coordinate. The following table shows several values for x and the function f evaluated at those numbers.
If we graph this relation, it looks like: Notice that you can draw a vertical line through the two points, like this: ... This graph does not show a function, because any number of vertical lines will intersect this oval twice. For instance, the y-axis intersects (crosses) the line twice.