But, the graph of y = x is to be drawn with some constraints. The constraint is that x ≥ 0. We should be aware that in which region x is greater than or equal to zero.
So, x is positive in the first quadrant that means that the portion of the graph lying in the 3rd quadrant is not valid since x is negative there.
Now, if we plot the graph of y = – x on the same graph with the condition x < 0.
So, the shape of graph of y = mod(x) is of ‘V’ sign.
Plotting of the graph of linear equation is dependent on the slope. In this case slope is of ±2, so still we will get a V-shaped figure only. Only difference being, since the slope is greater, we will get a steeper V figure.
Now, if we plot the graph of y = –x + 2 if x < 2.
Now, the origin has shifted to (–2) [origin is x = –2 because (x + 2) becomes zero at x = –2], so now the graph will shift horizontally on the left-hand side. Still the graph will be a V-shaped figure but it will made on the point (–2).
So, in all such horizontal movements, we need to find out points where the term inside the modulus will become zero. For e.g. (x – 2) becomes zero at x = 2 and ( x + 2) becomes zero at x = –2. And after finding out that we can just draw the V-shaped figure at those points.
Now this question is a combination of vertical and horizontal movements. If we have learnt the funda of horizontal and vertical movements well, we can plot the graph of this question easily.
Split the question in two parts in two parts. The graph will be a V-shaped figure whose origin on the X-axis will be +2 as [(x – 2) becomes zero at +2] and since the y-intercept is –3, the graph will be shifted downwards. And the V-shaped figure will be made at the intersection of the points (2, –3).
One thing which i would like to tell you guys while plotting this graph is that do not draw Y-axis. Because drawing Y-axis creates confusion as from where the lines of the graph will cut X-axis or Y-axis. So, let us see how to plot it.
In this case the graph will be a V-shaped made at (–2, –3) since the expression inside the modulus (x + 2) becomes zero at –2 and the y-intercept is –3.
Again while plotting the graph, do not plot the Y-axis.
