A-Math: How Do You Sketch A Modulus Graph?

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

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Hi, I'm Ai Ling Ong. I enjoy coaching students who have challenges with understanding and scoring in 'O' Level A-Maths and E-Maths. I develop Math strategies, sometimes ridiculous ideas to help students in understanding abstract concepts the fast and memorable way. I write this blog to share with you the stuff I teach in my class, the common mistakes my students made, the 'way' to think, analyze... If you have found this blog post useful, please share it with your friends. I will really appreciate it! :)

5 Responses to A-Math: How Do You Sketch A Modulus Graph?
  1. TYS
    May 15, 2009 | 6:06 pm

    In my opinion, student A diagram was wrong because he or she does not use equal scale for both x and y -axis. Thus, it has created the weird shape different from standard curve shape. However, I will agree with you in encouraging students to follow Student B's method for curve sketching.


  2. [...] I have written a similar post in 2009 here, I feel that a video will show you clearly the step by step and important points to consider. Note [...]

  3. Harry
    October 12, 2010 | 12:27 am

    How to sketch the graph y = |x+2|+|x-1|?


  4. Shivali
    November 14, 2011 | 1:55 pm

    How to sketch y = |x+3|+|x-6|?


  5. Andy
    May 3, 2013 | 7:39 pm

    Please explain me the graph of mode x plus mode y equals 1


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