EDGE Math 8

Vertical Line Test

Example 1

Graph $f (x) = x + 5.$ Then use the vertical line test to prove that it is a function.

Solution

The graph of $f (x) = x + 5$ is the graph of $y = x + 5.$ Construct a table of ordered pairs using the x-values –3, 0, and 3.

Value of x	Value of $f (x) = x + 5$	Ordered Pair $(x, y)$ or $(x, f (x))$
–3	$f (- 3) = 2$	$(- 3, 2)$
0	$f (0) = 5$	$(0, 5)$
3	$f (3) = 8$	$(3, 8)$

Plot the three points and draw a straight line through them. See the graph below.

You can now do the vertical line test. Note that if you draw vertical lines that pass through the graph, each of them will intersect the graph at no more than one point. Thus, $f (x) = x + 5$ is a function.