### Graphing Transformation

### Lesson 3: Modulus

(A)

The basic idea of a modulus function is to convert all negative values to its positive form. E.g. |-5| = 5. Hence this transformation will convert all the negative y coordinates of a graph to its positive value.

I.e. reflect the parts of the graph below the x axis upwards.

(B)

Notice that f (|-2|) = f(2). This means that for the graph of f (|x|), the y coordinates when x is negative is the same as when x is positive. This means the graph of f (|x|) is symmetrical about the y axis. To sketch the graph of f (|x|):

Step 1:

Erase the graph of f (x) when x < 0.

Step 2:

Draw a mirror image of the remaining graph on the right side onto the left.