help with graphing (1 Viewer)

[starryblue]

can anyone please explain to me how to graph reciprocal functions using limits? i really don't understand it. i don't understand what it means when any graph f(x) approaches zero plus or minus or infinite.

i also dont understand how to add or minus graph of y= f(x) + g(x)

sorry if i ask too many questions but i seriously don't get it eventhough so many people explained it to me already D:

 

[tohriffic]

Remember that for reciprocal functions, the new function is always the same sign as the original function and thus on the same side (in terms of positive and negative mind you)

(This is because 1/number will always give the sign of the number).

In terms of limits, understand that:




Because if you divide 1 by an infinitely large number, then the result is infinitely small. Think 1/9999.
Conversely,



Think 1/0.001.

When we say f(x) approaches infinity, then it is just continuously increasing and when it approaches 0, it is approaching the x axis. Just think of the y values you get from the reciprocal function.
For limits to infinity, the plus or minus indicates the sign of the resulting function.

For limits to 0, the plus or minus indicates the direction from which it approaches. 0+ is a little bit more than 0 and thus, it approaches the x axis from above.
0- is a little less than 0 so it approaches the x axis from below. I think all you have to remember is that f(x) and the reciprocal 1/f(x) lie on the same side. (Positive or negative)


Do you require more explanation? Sorry I'm not great at explaining things.