Identification of modulus function and cubic function — lesson. Mathematics State Board, Class 10.

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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:

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:

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6. Identification of modulus function and cubic function