Graphing Absolute Value Functions

To graph the desired function, we will make a table of values. To do so, we will assign some values to the $x -$ variable and calculate the corresponding values for $y .$

$x$	$∣ ∣ ∣ ∣ ∣ \frac{1}{3} x + 1 ∣ ∣ ∣ ∣ ∣$	$f (x) = ∣ ∣ ∣ ∣ ∣ \frac{1}{3} x + 1 ∣ ∣ ∣ ∣ ∣$
$- 12$	$∣ ∣ ∣ ∣ ∣ \frac{1}{3} (- 12) + 1 ∣ ∣ ∣ ∣ ∣$	$3$
$- 9$	$∣ ∣ ∣ ∣ ∣ \frac{1}{3} (- 9) + 1 ∣ ∣ ∣ ∣ ∣$	$2$
$- 6$	$∣ ∣ ∣ ∣ ∣ \frac{1}{3} (- 6) + 1 ∣ ∣ ∣ ∣ ∣$	$1$
$- 3$	$∣ ∣ ∣ ∣ ∣ \frac{1}{3} (- 3) + 1 ∣ ∣ ∣ ∣ ∣$	$0$
$0$	$∣ ∣ ∣ ∣ ∣ \frac{1}{3} (0) + 1 ∣ ∣ ∣ ∣ ∣$	$1$
$3$	$∣ ∣ ∣ ∣ ∣ \frac{1}{3} (3) + 1 ∣ ∣ ∣ ∣ ∣$	$2$

Now, we will plot and connect the obtained points on a coordinate plane. Recall that the graph of an absolute value function has a V shape.

We see above that the $x -$ variable can take any value. We also see that $y$ takes values that are greater than or equal to $0 .$ With this in mind, we can write the domain and range of the function. $Domain : Range : all real numbers y \geq 0$

Graphing Absolute Value Functions 1.17 - Solution