Property 3
Absolute Value Function
\(f(x)=|g(x)|\)
If \(a\in\mathbb R\) and \(g(a)=0\), point "a" is "f" function's critical point. Absolute value function could be written in piecewise function form.
Example
\(f(x)=|x|=\begin{cases}x&x\ge0\\-x&x<0\end{cases}\)
\(f(x)=|x-3|=\begin{cases}x-3&x>3\\-x+3&x\le3\end{cases}\)
Note
In absolute value function, equality will be written in the asked part.
In following, write down functions in piecewise form.
1.
\(f(x)=|x+4|\)
2.
\(f(x)=|2x-10|\)
3.
\(f(x)=|2x-1|\)
4.
\(f(x)=|5x+7|\)
5.
\(f(x)=\left|\samefrac{x-4}{2}\right|\)
6.
\(f(x)=|x^2-9|\)
7.
\(f(x)=|x^2-4x+3|\)
8.
\(f(x)=|x^2-4x|\)
9.
\(f(x)=|-x^2+x|\)