EDGE Math 8

Vertical Line Test

Example 5

Graph the following equation:

y^{2} = x

Then use the vertical line test on each graph to identify if its equation defines y as a function of x.

Solution

Construct a table of ordered pairs for the equation $y^{2} = x$ Solving for y gives $y = \pm \sqrt{x} .$ Solve for each value of y when 0, 1, and 4 are substituted to x.

Value of x	Value of $y = \pm \sqrt{x}$	Ordered Pair $(x, y)$
0	$y = - 0$	$(0, 0)$
1	$y = \pm 1$	$(1, 1)$ , $(1, - 1)$
4	$y = \pm \sqrt{4} = \pm 2$	$(4, 2)$ , $(4, - 2)$

Using the vertical line test, the graph of $y^{2} = x$ is that of a mere relation and not of a function.