Analyzing Graphs of Absolute Value Functions

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

$x$	$f (x) = - \frac{3}{5} ∣ x ∣$	Simplified Absolute Value	$f (x)$
$- 5$	$f (- 5) = - \frac{3}{5} ∣ - 5 ∣$	$f (- 5) = - \frac{3}{5} (5)$	$- 3$
$- 3$	$f (- 3) = - \frac{3}{5} ∣ - 3 ∣$	$f (- 3) = - \frac{3}{5} (3)$	$- 1.8$
$0$	$f (0) = - \frac{3}{5} ∣ 0 ∣$	$f (0) = - \frac{3}{5} (0)$	$0$
$3$	$f (3) = - \frac{3}{5} ∣ 3 ∣$	$f (3) = - \frac{3}{5} (3)$	$- 1.8$
$5$	$f (5) = - \frac{3}{5} ∣ 5 ∣$	$f (5) = - \frac{3}{5} (5)$	$- 3$

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

Analyzing Graphs of Absolute Value Functions 1.7 - Solution