Posted by **Ashley** on Monday, July 25, 2011 at 7:49pm.

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)

and f(x)= 3*2^x,

please explain everything, and if you use --> tell me what that means, cuz i have no clue

- Pre Cal -
**Damon**, Monday, July 25, 2011 at 8:08pm
--> 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

- Pre Cal -
**Ashley**, Monday, July 25, 2011 at 8:38pm
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?

- Pre Cal -
**Damon**, Monday, July 25, 2011 at 10:32pm
what is the big +x?

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

- Pre Cal -
**Ashley**, Tuesday, July 26, 2011 at 7:18am
ok, that's wahat i thought but wasn't sure.

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