Question

The given graph is an example of?

• A. Signum function
• B. Greatest Integer function
• C. Sinc function
• D. Exponential function

Answer 1

The correct option is A Signum function

From the graph we see that

• $f\left(x\right)=-1$ for $x<0$,
• $f\left(x\right)=0$ for $x=0$,
  
• $f\left(x\right)=1$ for $x>0$

That is $f\left(x\right)=\{\begin{array}{ccc}-1& for& x<0\\ 0& for& x=0\\ 1& for& x>0\end{array}$

Hence the function in the graph can be defined more precisely by $f\left(x\right)=\{\begin{array}{ccc}\frac{|x|}{x}& for& x\ne 0\\ 0& for& x=0\end{array}$ which is known as signum function.

Therefore the given graph represents signum function.