EDGE Math 8

Vertical Line Test

A graph is a tool used to visualize the behavior of a certain function. The graph of a function f is the graph of its ordered pairs $(x, y)$ in the rectangular coordinate system. You can graph a function by plotting its ordered pairs and drawing a line or a smooth curve through them.

Example

Graph $f (x) = x^{2} .$

Solution

The graph of $f (x) = x^{2}$ is the graph of $y = x^{2} .$ Construct a table of ordered pairs using the x-values –2, –1, 0, 1, and 2. For convenience, use integer values of x.

Value of x	Value of $f (x) = x^{2}$	Ordered Pair $(x, y)$ or $(x, f (x))$
–2	$f (- 2) = 4$	$(- 2, 4)$
–1	$f (- 1) = 1$	$(- 1, 1)$
0	$f (0) = 0$	$(0, 0)$
1	$f (1) = 1$	$(1, 1)$
2	$f (2) = 4$	$(2, 4)$

Now, plot the five points and draw a smooth curve through them. Note that the graph of f extends indefinitely to the left and to the right. Refer to the graph below.