Transformations of Absolute Value Functions

This is part of the HSC Mathematics Advanced course under the topic Functions and sub-part Graphing Techniques.

In this post, we apply transformations to sketch functions of the form $y=kf(a(x+b))+c$ , where $f(x)$ is a polynomial, reciprocal, absolute value, exponential or logarithmic function and $a,b,c$ and $k$ are constants:

Examine translations and the graphs of $y=f(x)+c$ and $y=f(x+b)$ using technology
Examine dilations and the graphs of $y=kf(x)$ and $y=f(ax)$ using technology
Recognise that the order in which transformations are applied is important in the construction of the resulting function or graph

Now, here is an example question on how to solve absolute value equations and inequalities and how to graph an absolute value function.