HSC Together Year 11 Maths Extension: Graphing Absolute Functions

#### Maths Extension

• Further Work with Functions
• Polynomials
• Inverse Trigonometric Functions
• Further Trigonometric Identities
• Rates of Change
• Working with Combinatorics
• Back to other subjects
Back to other subjects

# Graphing Absolute Functions

Graphing an absolute function is arguably the simplest kind of graphical transformation there is. This has two cases:

• y = |f(x)|
• y = f(|x|)

This is part of the Prelim Maths Extension 1 Syllabus from the topic Functions: Further, Work with Functions. In this post, we will explore graphical relationships of absolute functions

Here we will learn to examine the relationship between the graph of y= f(x) and the graphs of y= f|(x)| and y= f(|x|) and hence sketch the graphs.

Key points here include:

• An absolute function will turn any negative values to positive ones
• y= |f(x)| and y= f(|x|) will not always be the same
• y= |f(x)| will always have positive y values.
• y= f(|x|) can have negative y values and will look like its reflected across the y-axis.

Now let’s explore these concepts in the following videos.

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