Graphing Absolute Value Functions

a

Let's make the table of values for the function $f (x) = ∣ 3 x ∣ + 2 .$ 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.

$x$	$∣ 3 x ∣ + 2$	$f (x) = ∣ 3 x ∣ + 2$
$- 4$	$∣ 3 (- 4) ∣ + 2$	$14$
$- 3$	$∣ 3 (- 3) ∣ + 2$	$11$
$- 2$	$∣ 3 (- 2) ∣ + 2$	$8$
$- 1$	$∣ 3 (- 1) ∣ + 2$	$5$
$0$	$∣ 3 (0) ∣ + 2$	$2$
$1$	$∣ 3 (1) ∣ + 2$	$5$
$2$	$∣ 3 (2) ∣ + 2$	$8$
$3$	$∣ 3 (3) ∣ + 2$	$11$
$4$	$∣ 3 (4) ∣ + 2$	$14$

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 1.13 - Solution