Graphing Absolute Value Functions

In order to graph the given absolute value function, we can make a table of values.

$x$	$f (x) = ∣ x + 4 ∣ - 4$	Simplified Absolute Value	$f (x)$
$- 10$	$f (- 10) = ∣ - 10 + 4 ∣ - 4$	$f (- 10) = (6) - 4$	$2$
$- 8$	$f (- 8) = ∣ - 8 + 4 ∣ - 4$	$f (- 8) = (4) - 4$	$0$
$- 6$	$f (- 6) = ∣ - 6 + 4 ∣ - 4$	$f (- 6) = (2) - 4$	$- 2$
$- 4$	$f (- 4) = ∣ - 4 + 4 ∣ - 4$	$f (- 4) = (0) - 4$	$- 4$
$- 2$	$f (- 2) = ∣ - 2 + 4 ∣ - 4$	$f (- 2) = (2) - 4$	$- 2$
$0$	$f (0) = ∣ 0 + 4 ∣ - 4$	$f (0) = (4) - 4$	$0$
$2$	$f (2) = ∣ 2 + 4 ∣ - 4$	$f (2) = (6) - 4$	$2$

Now we can graph $f (x)$ by plotting the points and connecting them with straight lines on either side of the vertex.

Graphing Absolute Value Functions 1.6 - Solution