Question

Define modulus function. Draw the graph of Modulus function and writes its Domain and range.
CBSE XII

Answer 1

$\large\underline{\sf{Solution-}}$

Definition of Modulus function :-

$\begin{gathered}\begin{gathered}\rm :\longmapsto\:\bf\:y = |x| \: = \: \begin{cases} &\sf{x \: \: \: \: \: if \: x \geqslant 0} \\ &\sf{ - x \: \: if \: x < 0} \end{cases}\end{gathered}\end{gathered}$

Graph :-

Case 1.

$\rm :\longmapsto\:When \: x \geqslant 0 \:$

$\rm :\longmapsto\:y = x$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 0 \\ \\ \sf 1 & \sf 1 \\ \\ \sf 2 & \sf 2 \end{array}} \\ \end{gathered}$

Case :- 2.

$\rm :\longmapsto\:When \: x < 0$

$\rm :\longmapsto\:y = - \: x$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf - 1 & \sf 1 \\ \\ \sf - 2 & \sf 2 \\ \\ \sf - 3 & \sf 3 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points.

➢ See the attachment graph.

Domain

$\rm :\longmapsto\:Domain \: of \: |x| \: is \: x \: \in \: R$

Range

$\rm :\longmapsto\:Range \: of \: |x| \: is \: x \: \in \: [0, \: \infty )$