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.
Part 1
Part 2
Part 3
