what does it mean when it says describe the end behavior of f and whats that for f(x)=(x^2+x+3)/(x-1)

Question

and f(x)= 3*2^x,
please explain everything, and if you use --> tell me what that means, cuz i have no clue

Answer 1

--> means "goes to"
as in what happens to your function there as x goes to 1
or as x --> 1

As x -->1
The numerator becomes 1+1+3 = 5
so the function looks like 5/(x-1)
but of course x-1 is 0 when x =1 so the function becomes undefined when x = 1
but what if x = 1.001 for example
then the function is about
5/.001 or 5000
and if x = .0001
then it is about 50,000 very big
Now look at x = .999
then it is 5/-.001 = -5000
and if x = .9999 then f = -50,000
do we see a trend here?
graph it.
Now what happens as x-->oo
when x is big, x^2 is much bigger than x or 3
so the numerator looks like x^2
similarly the denominator looks like x
so for big +x the function looks like just plain old x, a straight line of slope +1
And if you do x-->-oo
then the numerator is positive x^2 and the denominator looks like x so the result is again looks like x, that same straight line of slope +1

Answer 2

what is the big +x?
and so the answer is
"so for big +x the function looks like just plain old x, a straight line of slope +1" and "then the numerator is positive x^2 and the denominator looks like x so the result is again looks like x, that same straight line of slope +1"? if so is there an easier way to write that?

Answer 3

what is the big +x?

In other words what happens when x is a large positive number.

Answer 4

ok, that's wahat i thought but wasn't sure.