3 The modulus function

The modulus of a number is the size of that number with no regard paid to its sign. For example the modulus of $-7$ is 7. The modulus of $+7$ is also 7. We can write this concisely using the modulus sign $\left|\right|$ . So we can write $|-7|=7$ and $|+7|=7$ . The modulus function is defined as follows:

The output from the function in Key Point 14 is simply the modulus of the input.

A graph of this function is shown in Figure 32.

Figure 32 :

Task!

Draw up a table of values of the function $f\left(x\right)=\left|x-2\right|$ for values of $x$ between $-3$ and 5. Sketch a graph of this function.

Exercises

1. Sketch a graph of the following functions:
   1. $f\left(x\right)=3\left|x\right|$ ,
   2. $f\left(x\right)=|x+1|$ ,
   3. $f\left(x\right)=7|x-3|$ .
2. Is the modulus function one-to-one or many-to-one?

Answer