# Thread: How do I do this?

1. ## How do I do this?

a) Determine the value the function f approaches as the magnitude of x increaces. Is f(x) greater than or less than this functional value when (b) x is positive and large in magnitude and (c) x is negative and large in magnitude.
f(x) = 2 + (1)/(x-3)

Ok, so apparently this question has three parts; a, b, and c. I honestly don't understand how to solve this question. I am online school and I cannot contact my teacher right now, but I still have to submit the assignment.

How do I solve this question?
Thanks

2. $\displaystyle f(x)=2+\frac{1}{x-3}$

As x gets large, $\displaystyle f(x)\rightarrow 2$ (this is the same question as the $\displaystyle \lim_{x\rightarrow\infty} f(x)$

If you are uncomfortable with that limit, think of it this way: As x gets huge, the denominator of the fraction gets huge and 1 divided by a huge number is basically zero. So the function approaches 2+0=2

When x is positive and large in magnitude, we have the situation i described above, x goes to infinity, so the denominator of the fraction becomes huge and positive. Now they ask is f(x) greater or not, and the answer is since the fraction is positive, even though it's essentially zero, f(x) is greater than this functional value (think of 2+.00000000000001>2)

You should be able to do part c). As gets gets huge in the negative direction, the fraction will still aproach zero but the fraction will now be __________ so f(x) is ___________ than this functional value