.

Question

.

anonymous · Answer

use the y=mx+b function

dape · Answer

Yes, the domain is the possible x's and the range the possible y's.

anonymous · Answer

m=slope b=the y intercept in the y=mx+b function. It really comes in handy when your graphing @Bergsterr

dape · Answer

x can also be negative, so x≠0 is the domain. The range actually include all numbers, which can be hard to see. To graph you need to learn by heart how the function $\frac{1}{x}$ looks. Which you can see here: http://www.wolframalpha.com/input/?i=plot+1%2Fx

dape · Answer

I would write $y\in\mathbb{R}$. This just reads 'y is a real number'.
But you can also write it like an interval like this $y\in(-\infty,\infty)$, which reads 'y is in the range from negative infinity to infinity'

dape · Answer

You can just write $(-\infty,\infty)$ in the range part on your paper.

dape · Answer

So you need to understand how functions transform under translation. In other words, what happens to the x's and y's when you move the graph around in the plane. So starting from $$y=\frac{1}{x}$$ We can shift this graph down by two by subtracting 2 on the right hand side, so the graph of $$y=\frac{1}{x}-2$$ Is just 1/x shifted two steps down. Then a minus sign in front of the x like this $$y=\frac{1}{-x}-2=-\frac{1}{x}-2$$ Just flips the graph upside down. Here it is: http://www.wolframalpha.com/input/?i=plot+-1%2Fx-2%2C+x+from+-2+to+2

dape · Answer

You are comparing the graphs.