Question

Determine the end behavior of f(x) = e^x

Answer 1

what happens to f(x) when x is very very large. Does it get bigger or smaller?

Answer 2

Bigger

Answer 3

Correct!

How much bigger?

Look at a few samples here for low values, how much bigger do you think e^x is for LARGE values of X.

$$
\large {
e^0=1\\
e^1=2.7\\
e^2=7.4\\
e^3=20.1\\
...
}$$

Do you think this will end up at some point at a single number?

Answer 4

Well it is growing exponentially. So really really really huge. I suppose it could end up as a single number.

Answer 5

What is the largest number you can think of?