The graph of $y=f(x)$ for $-3\le x\le 3$ is shown below. On this interval, what is the range of $f(x)-x$? Express your answer in interval notation.

 Jul 26, 2018

Note that  in each  "piecewise"  part of the function, the  greatest value of  [f(x)  - x]  occurs at the left part of the interval  and is   0


And note that the least value of  f(x)  - x  occurs at the right part of the piecewise interval and is  "almost"  -1


So...the range of  f(x)  - x   is  ( -1, 0 ] 



cool cool cool

 Jul 26, 2018

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