Last Sunday while coaching my A-Math students on a question on Modulus Functions, we did solving of Modulus equation which is of no big problem as long as you get the basic concept correct.
|x| = x when x >= (more than and equal to) 0 or |x| = -x when x < 0
When we came to the next part of the question which involves Sketching of Modulus Graph, that's where the interesting happens.
Read about the Differences between Drawing and Sketching in this post.
When question involves sketching of graph, we usually do not need
- a table of values.
- axis which are evenly marked out.
Sketching of Graph should however includes
- critical points (i.e x - intercept(s), y-intercept, turning point (if you are sketching a quadratic graph))
Let's take a look at the working of 2 different students:
Student A:
- Sketch the modulus graph using table of values
- Join up the points in a straight line manner
Student B:
- Sketch the modulus graph using a series of 2 other graphs
Note the difference in the shape of the 2 graphs.
I certainly hope that my student A is convinced that using a table of values is not recommended for drawing modulus graphs. Moreover, many questions involving modulus could be that of Trigonometry graphs! So be like student B, draw modulus graph using a transformation of a series of graphs