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Modulus Function or Absolute valued Function:
A function \(f: \mathbb{R} \rightarrow [0, \infty)\) defined by \(f(x) = |x|\).
Where \(f(x) = \begin{cases} x & , x\geq 0 \\ -x & , x<0 \end{cases}\)
The graphical representation of the modulus or absolute valued function is given by:
modulus functionx.png
Cubic Function:
A function \(f: \mathbb{R} \rightarrow \mathbb{R}\) defined by \(f(x) = ax^3 + bx^2 + cx + a\), \((a \neq 0)\) is called a cubic function.
\(f(x) = x^3\) is an example of a cubic function.
This function is graphically represented as follows:
Cubic function.png