A graph of the given absolute value function |3w + 3| ≤ 9 is shown on the number line in the picture below.
In Geometry, a number line refers to a type of graph that is composed of a graduated straight line, which typically comprises both negative and positive numerical values (numbers) that are located at equal intervals along its length.
This ultimately implies that, every number line would primarily increase in numerical value towards the right from zero (0) and decrease in numerical value towards the left from zero (0).
Based on the information provided above, we can logically deduce the following absolute value function:
|3w + 3| ≤ 9
3w + 3 ≤ ±9
3w ≤ 9 - 3
3w ≤ 6
w ≤ 2
3w ≥ -9 - 3
3w ≥ -12
w ≥ - 4
-4 ≤ w
In this exercise, we would use an online graphing calculator to plot the given points as shown on the number line (graph) attached below.