can anyone possibly explain to me how to go about figuring out the answer. to be specific i dont just want the answer i need to know how to figure it out for myself lol

You use KhanAcademy! I find them a maze of information: it's difficult to find the right bit, but once you found it, it's valuable all right!

The domain are the values your function can assume. For a linear equation, you can imagine that any x value is valid: All real values of t are viable options to stuff into your equation without there being a contradiction or a mathematical impossibility.
Consider f(x) = 1/(x+3)
One cannot divide by zero, therefore x may never equal -3. Your domain would be all real values of x except for x = -3.
This goes for any division: your denominator may not equal zero. If there is a value for x where this is the case, it will be the value that is not in your domain.

Similarly, you know log functions cannot have 0 or a negative number and squareroots won't work well with negative numbers.

/e You'll find horizontal asymptotes by simply stuffing in a silly big x value and see where your answer is going to. For slant asymptotes you need polynomial divisions, but from the looks of your exercise I don't think it's relevant as of yet. If it is, you can find it here: http://www.purplemath.com/modules/asymtote3.htm

The domain of a function is determined by values for the variable that a function is not allowed to assume.

This post was edited by Forg0tten on May 28 2017 02:34pm

all reals
It's a polynomial

Lim g (t) tends to -inf or +inf as t approaches -inf or inf

This post was edited by Zekdawg on May 28 2017 06:24pm

graph the function either on your calculator (should know how to do this for tests) or wolfram alpha

look at the graph and see if the graph is continuous on the x-axis (there are no holes or missing spots)----if you can "zoom out" and the graph keeps going in both directions then its all real numbers/values