Property 4
Signum Function
\(x\in\mathbb R\)
\(\operatorname{sgn}(x)=\begin{cases}1&x>0\\0&x=0\\-1&x<0\end{cases}\)
\(f(x)=\operatorname{sgn}(g(x))=\begin{cases}1&g(x)>0\\0&g(x)=0\\-1&g(x)<0\end{cases}\)
If \(a\in\mathbb R\) and \(g(a)=0\), point "a" is function critical point.
1.
\(\operatorname{sgn}(\pi)=?\)
2.
\(\operatorname{sgn}(x-6)=1\)
\(S.S.=?\)
3.
\(\operatorname{sgn}(x^2-16)=0\)
\(S.S.=?\)
4.
\(\operatorname{sgn}(x+7)=-1\)
\(S.S.=?\)
5.
\(x\in\mathbb R\)
\(\operatorname{sgn}(x^2+x+1)=?\)
6.
\(x\in\mathbb R\)
\(\operatorname{sgn}(x^2+4)=?\)
In following given functions , write them down in piecewise function form.
1.
\(f(x)=\operatorname{sgn}(x-6)\)
2.
\(f(x)=\operatorname{sgn}(x+4)\)
3.
\(f(x)=\operatorname{sgn}(x^2-16)\)
4.
\(f(x)=\operatorname{sgn}(x^2-5x+4)\)