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Graphing Absolute Value Functions

Absolute Value Functions

Graphing Absolute Value Functions 1.14 - Solution

Return to 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 $y .$ For simplicity, we will use multiples of $3$ so that the values of $y$ are integers. Make sure to include positive and negative numbers, as well as zero.

$x$	$- \frac{3}{4} ∣ x + 4 ∣ - 2$	$f (x) = - \frac{3}{4} ∣ x + 4 ∣ - 2$
$- 16$	$- \frac{3}{4} ∣ - 16 + 4 ∣ - 2$	$- 11$
$- 12$	$- \frac{3}{4} ∣ - 12 + 4 ∣ - 2$	$- 8$
$- 8$	$- \frac{3}{4} ∣ - 8 + 4 ∣ - 2$	$- 5$
$- 4$	$- \frac{3}{4} ∣ - 4 + 4 ∣ - 2$	$- 2$
$0$	$- \frac{3}{4} ∣ 0 + 4 ∣ - 2$	$- 5$
$4$	$- \frac{3}{4} ∣ 4 + 4 ∣ - 2$	$- 8$
$8$	$- \frac{3}{4} ∣ 8 + 4 ∣ - 2$	$- 11$

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.