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  1. ${y\over|y|}={x\over|x|}$
  2. ${\lfloor x \rfloor \lfloor y \rfloor = 1}$

Determine if each graph represents a function of x and explain your answer.

I've never seen anything like the before and I'm not sure where to start.

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Try distinguishing cases: positive $y$, negative $y$, postive $x$, negative $x$ to get rid of the absolute values, and do a similar thing for the floor function. – dreamer Mar 16 '14 at 9:26
Don't tell me what to do. – Mike Miller Mar 16 '14 at 9:40


  1. ${y\over|y|}={x\over|x|}$ \begin{cases} x \ge 0 \Rightarrow \frac{x}{|x|} = \frac{y}{|y|} = 1 \Rightarrow y \ge 0 \\ x \lt 0 \Rightarrow \frac{x}{|x|} = \frac{y}{|y|} = -1 \Rightarrow y \lt 0 \\ \end{cases} So ${y\over|y|}={x\over|x|}$ is a general way to refer to every functions whose graph is in the $I$ and $III$ quadrant of a Cartesian coordinate system.
  2. ${\lfloor x \rfloor \lfloor y \rfloor = 1} \Rightarrow \lfloor y \rfloor = \frac{1}{\lfloor x \rfloor} \ldots$
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