Taking the absolute value of a number is equivalent to ignoring any minus sign, We are only interested in the magnitude of a number. For example,
We sometimes have to sketch graphs of the form
The graph of is a straight line. When , . If , for example if , then which is greater than zero. We can plot the point .
If then . This is less than zero. We are plotting the values of against absolute values of y, so we find the absolute value of which is 1 and plot the point, . At the point where is zero, on one side of which it would be negative, and on the other side positive, if were were plotting a line and not an absolute value graph, there will be a “corner”.
We can draw up the set of values of x and y. They are given below next to the graph.
In general to sketch any graph of this sort we can start by finding the zero: there will be a corner at that point. On either side of the corner will be a straight line. It is then enough to find one point either side of the corner to draw the graph..
Finding the corner can sometimes be tricky, but you ownly have to find where the modulus part is zero.
For the graph the corner is when at the point
For the graph the corner is when , at the point , shown below.