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In the chapter Transformations of the book College Algebra by Michael Sullivan i've seen two paragraph-

When the right side of the function $y=f (x)$ is multiplied by $-1$, the graph of the new function $y=-f(x)$ is the reflection about the x-axis of the graph of the function $y=f(x)$.

When the graph of the function $y=f(x)$ is known the graph of the new function $y=f(-x)$ is the reflection about y-axis of the graph of the function $y=f(x)$.

In the new function $\lfloor x\rfloor$ i see that two cases exist. First case happen when $x>0$ and the second case when $x<0$ .

If i follow these two paragraphs for these two intervals i ended up with wrong graph. I know that i am wrong in some part of the whole idea but don't know in which part.

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  • $\begingroup$ What is $int(x)$? The greatest-integer function, aka floor or $\lfloor x\rfloor$? $\endgroup$ – Hagen von Eitzen Jun 8 '18 at 5:14
  • $\begingroup$ Hagen von Eitzen , Yes, it's Greatest Integer Function $\endgroup$ – Noman Jun 8 '18 at 5:15
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Let $f(x)=\lfloor x \rfloor$, then $f(-x) = \lfloor -x \rfloor$.

Hence if the reflection about the $y$-axis.enter image description here

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  • $\begingroup$ Does reflection about x-axis also exist? $\endgroup$ – Noman Jun 8 '18 at 5:28
  • $\begingroup$ It exists, but it is not the same function. $\endgroup$ – Siong Thye Goh Jun 8 '18 at 5:31

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