Mastering Modulus Graph Transformations

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Mastering Modulus Graph Transformations

Learning objective

Learning Objective

At the end of the lesson, you will understand and sketch transformations of modulus graphs, including y = af(x), y = f(x) + a, y = f(x + a), y = f(ax).

What do you already know about transforming graphs?

Understanding Modulus Functions

Modulus functions reflect negative values to positive. For y = |f(x)|, all y-values are non-negative.

Transformation: y = af(x)

Scaling factor 'a' vertically stretches if a > 1 or compresses if 0 < a < 1.

Transformation: y = f(x) + a

Adding 'a' shifts the graph vertically. Positive 'a' moves it up; negative 'a' moves it down.

Transformation: y = f(ax)

Factor 'a' compresses horizontally if a > 1 or stretches if 0 < a < 1.

Transformation: y = f(x + a)

Adding 'a' inside the function shifts the graph horizontally. Positive 'a' moves it left.

Combining Transformations

Graphs can have multiple transformations. Apply each step-by-step to understand the overall effect.

Example Problem 1

Sketch y = 2|x + 1| - 3. Identify transformations: vertical stretch, horizontal shift, vertical shift.

Example Problem 2

Sketch y = |3x - 2|. Apply horizontal compression and horizontal shift transformations.

Given the function y = |x|, sketch the graph of y = 2|x|. Describe how the graph has been transformed from the original.

Given the function y = |x|, sketch the graph of y = |2x|. What effect does this have on the graph?

Consider the function y = |x|. Sketch the graph of y = |x - 2|. Explain the transformation applied.

For the function y = |x|, sketch the graph of y = |x| + 3.

What transformation has been applied to the original graph?

Sketch the graph of y = 3|x + 1| - 4. Describe each transformation step by step from the original graph y = |x|.

Summary and Q&A

Summarise key points. Questions? Clarify any doubts about modulus graph transformations.

Write down 3 things you learned in this lesson.

Write down 2 things you want to know more about.

Ask 1 question about something you haven't quite understood yet.