Answer to Question #347871 in Calculus for Stella

Question #347871

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


f(x) = |x|•|x-1|

1
Expert's answer
2022-06-12T15:41:50-0400
x<0,f(x)=x(1x)=x2xx<0, f(x)=-x(1-x)=x^2-x

0x<1,f(x)=x(1x)=x2+x0\le x<1, f(x)=x(1-x)=-x^2+x

x1,f(x)=x(x1)=x2xx\ge1, f(x)=x(x-1)=x^2-x

f(x)={x2xx<0x2+x0x<1x2xx1f(x)= \begin{cases} x^2-x &x<0 \\ -x^2+x &0\le x<1\\ x^2-x & x\ge1 \end{cases}


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