Mathematics - Functions Question with Solution | TestHub

Given: $f(x)=(-1{)}^{[x]}$. First of all, we sketch the graph of $f(x)$ with the help of piecewise defined functions as follows:

$$f(x)=(-1{)}^{[x]}=\{\begin{array}{cc}1;& -2\le x<-1\\ -1;& -1\le x<0\\ 1;& 0\le x<1\\ -1:& 1\le x<2\\ 1;& 2\le x<3\end{array}$$

The graph of $f(x)$ is given by From the above graph of $f(x)$, we see that the function $f(x)$ repeats its value after the least interval of 2. Therefore the function $f(x)$ is periodic with period 2.