Question

Find equivalent functional definition for each of the following and draw a graph of the function.

f(x) = |x|•|x-1|

Answer 1

$$x<0, f(x)=-x(1-x)=x^2-x$$

$$0\le x<1, f(x)=x(1-x)=-x^2+x$$

$$x\ge1, f(x)=x(x-1)=x^2-x$$

$$f(x)= \begin{cases} x^2-x &x<0 \\ -x^2+x &0\le x<1\\ x^2-x & x\ge1 \end{cases}$$