Q.
Consider the following statements
Statement I The graph of modulus function is
Statement II The Signum function is $f: R \rightarrow R$ defined by $f(x)=[x]$.
Choose the correct option.
Relations and Functions
Solution:
I. The modulus function The function $f: R \rightarrow R$ defined by $f(x)=|x|$ for each $x \in R$ is called modulus function. For each non-negative value of $x, f(x)$ is equal to $x$. But for negative values of $x$, the value of $f(x)$ is the negative of the value of $x$, i.e.,
The graph of the modulus function is given in above figure.
II. Signum function The function $f: R \rightarrow R$ defined by
$f(x)=\begin{cases}1, \text { if } x>0 \\ 0, \text { if } x=0 \\ -1, \text { if } x< 0\end{cases}$
is called the signum function. The domain of the signum function is $R$ and the range is the set $\{-1,0,1\}$. The graph of the signum function is given by the figure.
