In which way should i transform int(x) (Greatest Integer Function) into int(-x)?

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.

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

Let $f(x)=\lfloor x \rfloor$, then $f(-x) = \lfloor -x \rfloor$.
Hence if the reflection about the $y$-axis. 