The document discusses modulus (absolute value) functions, including that the modulus function f(x)=|x| has a domain of all real numbers and a range of zero to infinity. It is symmetrical about the y-axis and has a sharp point at the origin. Transformations to the modulus function involve dilation by a factor a and vertical translation by an amount c. A modulus function can also be expressed as two separate functions, one for negative values of f(x) and one for positive values of f(x).

1. Maths Methods
Modulus (Absolute Value) Functions
K McMullen 2012

2. Modulus Functions
The function f(x)=|x| is called the modulus or
absolute value function
The domain is R
The Range is [0, ∞)
The graph is symmetrical is the y-axis and has a
cusp (sharp point) at the origin
K McMullen 2012

3. Modulus Functions
Transformations of the modulus function:
y=a|f(x)|+c
a is the dilation factor
c is the vertical translation
To draw the modulus function
Draw f(x)
Reflect f(x) along the x-axis to get |f(x)|
Then do your transformations
K McMullen 2012

4. Modulus Functions
A modulus function can be thought of as two
separate expressions, depending on whether it is
negative or positive
To show the two parts of a modus function you
need to set up a hybrid function
One for: f(x)<0
One for: f(x)>0
To determine the particular values of x, you need
to solve the two inequalities
The hybrid function basically shows the domain of
the modulus function
K McMullen 2012