Question

How do you find the right end behavior model and left end behavior model for f(x)=x+(e^x)

Answer 1

\[f(x)=x+e ^{x}\]

Answer 2

end behaviour as in what happens when \(x\to \infty\) ?

Answer 3

what do you think happens?

Answer 4

I mean, I know what the graph of f(x)=e^x looks like, so I figured it'd look the same, but the answers my textbook gives are different than what I thought end behavior was. They're asking for a function to model it after I guess, which I don't really get how you would know

Answer 5

if \(x\to\infty\) then \(x+e^x\to \infty\) as well right?

Answer 6

pretty damn fast in fact

Answer 7

Yeah

Answer 8

and as \(x\to -\infty\) \(x+e^x\to -\infty\) since \(x\to -\infty\) and \(e^x\to 0\)

Answer 9

Um, I think that's where I'm lost. I know that as x approaches negative infinity, e^x approaches 0, but how would the x added to e^x in this function affect the end behavior to make the function approach negative infinity instead?

Answer 10

it does go to minus infinity

Answer 11

the \(e^x\) term goes to zero

Answer 12

That's what I'm asking- why does it go to minus infinity? I know that e^x goes to zero, so why does x+e^x go to negative infinity?

Answer 13

because \(x\) is going to negative infinity and \(-\infty+0=-\infty\)

Answer 14

OH. Wow. My dunce moments are at an all time high tonight. Haha. But this is the part that really trips me up about the question. It's looking for an end behavior MODEL. So I know the answers- the right end behavior model is e^x and the left end behavior model is x, but why? How am I supposed to just know that?

Answer 15

no ideas, except that maybe \(e^x\) grow way way faster than \(x\)

Answer 16

i guess what they are saying is that as \(x\to -\infty\) the function
\[x+e^x\] looks like \(x\)

Answer 17

whereas if \(x\to \infty\) it looks like \(e^x\)