Graphing Absolute Value Functions

a

Let's make the table of values for the function $f (x) = ∣ 2 x - 1 ∣ .$ In this case, $x$ will take integer values from $- 4$ to $4,$ inclusive. Recall that integers are a set of numbers that consist of all real numbers, negative, positive and zero that do not contain any decimal parts.

$x$	$∣ 2 x - 1 ∣$	$f (x) = ∣ 2 x - 1 ∣$
$- 4$	$∣ 2 (- 4) - 1 ∣$	$9$
$- 3$	$∣ 2 (- 3) - 1 ∣$	$7$
$- 2$	$∣ 2 (- 2) - 1 ∣$	$5$
$- 1$	$∣ 2 (- 1) - 1 ∣$	$3$
$0$	$∣ 2 (0) - 1 ∣$	$1$
$1$	$∣ 2 (1) - 1 ∣$	$1$
$2$	$∣ 2 (2) - 1 ∣$	$3$
$3$	$∣ 2 (3) - 1 ∣$	$5$
$4$	$∣ 2 (4) - 1 ∣$	$7$

b

Now, we will plot the obtained points on a coordinate plane.

c

To graph the function, we will connect the plotted points. Recall that the graph of an absolute value function has a V shape.

Graphing Absolute Value Functions 1.15 - Solution