Question

Consider the following statements
Statement I The graph of modulus function is

Statement II The Signum function is $f:R\to R$ defined by $f(x)=[x]$.
Choose the correct option.

• A. Statement I is true
• B. Statement II is true
• C. Both are true
• D. Both are false

Answer 1

Answer: (D)

I. The modulus function The function $f:R\to R$ 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 $f:R\to R$ defined by
$f(x)=\{\begin{array}{l}1,\text{ if }x>0\\ 0,\text{ if }x=0\\ -1,\text{ if }x<0\end{array}$
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.