## amyna one year ago 1) e^-x has domain all real numbers = true why?? 2) e^-x has range all real numbers = false why?? can someone please explain why the above is true and the other is false? i need to explain why

1. zepdrix

Do you understand why 1) is true? We can work out why 2) is false, but do you understand 1)? Domain is the x values that we're allowed to plug into the function.

2. amyna

yes, i forgot domain were the x values lol

3. zepdrix

For the outputs, the y values, the range, just try plugging in some values to get an idea of what is going on.|dw:1444275760273:dw|

4. zepdrix

When I plug in negative x's, the function is blowing up real fast. So the range certainly contains all of the positive numbers 1 and above. But it looks like something it happening at zero, ya?

5. amyna

yes, but how should i word my explanation for both?

6. zepdrix

Hmm :d

7. amyna

ya thats the hard part

8. zepdrix

Ok umm I remember a problem you did a while back with monotonicity, ya? Maybe we can apply that idea here. Say something about the fact that the function is monotonically decreasing, and $$\large\rm \lim\limits_{x\to\infty}e^{-x}=0$$ So since the function is decreasing, and doesn't diverge to negative infinity, it's doesn't include all of the real numbers for the range.

9. zepdrix

I dunno, just an idea ^

10. amyna

alrighty ! i'll come up with something eventually! Thank you! :)

11. zepdrix

:3