Assignment #92: Applying The Vertical Line Test
The Cartesian coordinate system has the virtue of easily revealing whether a relation is a
function. If one sees a point directly above another point, this means that the two points have
the same x-coordinate, and hence the relation is not a function. Another way to say this is that
if a vertical line could be placed on the graph in such a way as to touch more than one point in
the relation, then the relation is not a function. This method of determination is called the
vertical line test.
Reminder: To graph a non-linear function make an X/Y table and use x = 0, y = 0, +big and –big,
and pay attention to the denominator to figure out possible asymptotes. Then use a range of
values of x that occur on both sides of any vertical asymptotes in order to see how the graph is
going to curve.
Problems for Assignment #92:
For problems #1 – 4 please write whether the graph represents a function or not.
For problems #5-7, please sketch each graph on a separate set of axes by making points. [Hint:
Be aware that in problem 5, we cannot use x = 1 or x = 4. These values would generate zero in
the denominator, and division by zero is undefined. Find some way to represent on the graph
the fact that we cannot use x = 1 or x = 4. Remember how we drew asymptote lines in class.]
2x-1
5. y = (x-1)(x-4)
x
6. y = 2
x +1
7. y =
1
1 x2
(Optional): The capacity of an elevator is either 20 children or 15 adults. If 12 children are
currently on the elevator, how many adults can get on?