Graphing Absolute Value Functions

We are asked to draw the graph of $f (x) = - ∣ x + 3 ∣ - 2 .$ To do so, we will use a table of values to find points on the graph. Recall that the absolute value removes the negative sign. In this case, however, we have a negative sign preceding the absolute value. This will take each positive value created by the absolute value and then make it negative, regardless of its original sign.

$x$	$- ∣ x + 3 ∣ - 2$	Simplify absolute value	$f (x) = - ∣ x + 3 ∣ - 2$
$- 7$	$- ∣ - 7 + 3 ∣ - 2$	$- (4) - 2$	$- 6$
$- 5$	$- ∣ - 5 + 3 ∣ - 2$	$- (2) - 2$	$- 4$
$- 3$	$- ∣ - 3 + 3 ∣ - 2$	$- (0) - 2$	$- 2$
$- 1$	$- ∣ - 1 + 3 ∣ - 2$	$- (2) - 2$	$- 4$
$1$	$- ∣ 1 + 3 ∣ - 2$	$- (4) - 2$	$- 6$

Now, we will plot and connect the obtained points. Doing that we keep in mind that the graph of an absolute value function has a V shape.

Graphing Absolute Value Functions 1.9 - Solution