Modulus Transformations (DP IB Analysis & Approaches (AA)): Revision Note

Modulus Transformations

How do I sketch the graph of the modulus of a function: y = |f(x)|?

• STEP 1: Keep the parts of the graph of y = f(x) that are on or above the x-axis

• STEP 2: Any parts of the graph below the x-axis get reflected in the x-axis

How do I sketch the graph of a function of a modulus: y = f(|x|)?

• STEP 1: Keep 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|)?

• 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 x-axis

  • It can go below the x-axis

When multiple transformations are involved how do I determine the order?

• The transformations outside the function follow the same order as the order of operations

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    • Deal with the a then the b then the modulus

  • 

    • Deal with the modulus then the a then the b

• The transformations inside the function are in the reverse order to the order of operations

  •  

    • Deal with the modulus then the b then the a

  • 

    • Deal with the b then the a then the modulus