Sketching Graphs of Modulus Functions (Edexcel International A Level (IAL) Maths): Revision Note
Did this video help you?
Modulus Functions - Sketching Graphs
Modulus functions
The modulus function makes any ‘input’ positive
|x| = x if x ≥ 0 |f(x)| = f(x) if f(x) ≥ 0
|x| = -x if x < 0 |f(x)| = -f(x) if f(x) < 0
For example: |5| = 5 and |-5| = 5
Sometimes called absolute value
How do I sketch the graph of the modulus function: y = a |x + p| + q?
The graph will look like a “ꓦ” if a > 0 or a “ꓥ” if a < 0
There will be a vertex at the point (-p, q)
There could be 0, 1 or 2 roots
This depends on the location of the vertex and the orientation of the graph (ꓦ or ꓥ)
Compare this to the completed square form of a quadratic a(x + p)² + q

How do I sketch the graph of the modulus of a function: y = |f(x)|?
STEP 1 Pencil in the graph of y = f(x)
STEP 2 Reflect anything below the x-axis, in the x-axis, to get y = |f(x)|

How do I sketch the graph of a function of a modulus: y = f(|x|)?
STEP 1 Sketch the graph of y = f(x) only for x ≥ 0
STEP 2 Reflect this in the y-axis

What is the difference between y = |f(x)| and y = f(|x|)?
There is a difference between y = |f(x)| and y = f(|x|)
The graph of y = |f(x)| never goes below the x-axis
It does not have to have any lines of symmetry
The graph of y = f(|x|) is always symmetrical about the y-axis
It can go below the y-axis

Worked Example

Unlock more revision notes. It's free!
By signing up you agree to our Terms and Privacy Policy.
Already have an account? Log in
Did this page help you?