Final answer:
The statement that the graph of f(x) = |3x+2| is a horizontal line is incorrect. The graph of an absolute value function is V-shaped, not horizontal, with a pivot at the point where the value inside the absolute becomes zero.
Step-by-step explanation:
The claim that the graph of f(x) = |3x+2| is a horizontal line is not correct. The absolute value function typically results in a graph with a 'V' shape, due to the nature of absolute value creating a positive output for both positive and negative inputs. When graphing f(x) = |3x+2|, there will be a pivot at the point where the expression within the absolute value is zero, which in this case occurs when 3x + 2 = 0, or x = -2/3. For x values less than -2/3, the graph will be an increasing line, and for x values greater than -2/3, the graph will also be an increasing line but in the positive direction of the y-axis because of the absolute value.
To clearly illustrate this, for 0 ≤ x ≤ 20, the graph will show a steady incline starting at the point (0, f(0)) which is (0, |3*0+2|) = (0, 2) to the point (20, f(20)) which is (20, |3*20+2|) = (20, 62), passing through the pivot point located at (-2/3, 0). It is important to note that quadratic equations and vector diagrams mentioned in the supplementary information do not directly relate to absolute value functions, and the behavior of this specific function.