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# help asap pls (1 question only)

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1.) The function $\lfloor x\rfloor$ is defined as the largest integer less than or equal to $x$. For example, $\lfloor 5.67\rfloor = 5$, $\lfloor -\tfrac 14\rfloor = -1$, and $\lfloor 8\rfloor = 8$.What is the range of the function $$f(x) = \lfloor x\rfloor - x~?$$Express your answer in interval notation.

$$\text{Problem (with }\LaTeX)$$

The function $$\lfloor x\rfloor$$ is defined as the largest integer less than or equal to $$x$$. For example, $$\lfloor 5.67\rfloor = 5$$, $$\lfloor -\tfrac 14\rfloor = -1$$, and $$\lfloor 8\rfloor = 8$$.What is the range of the function

$$f(x) = \lfloor x\rfloor - x~?$$

Express your answer in interval notation.

Apr 27, 2019
edited by lolzforlife  Apr 28, 2019
edited by lolzforlife  Apr 28, 2019

### 1+0 Answers

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$$f(x) = \lfloor x\rfloor - x$$

The floor of x is less then or equal to x with a difference of less than 1

So the subtraction will result in a number between -1 and 0

The range is     (-1,0]

May 1, 2019