amyna
  • amyna
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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zepdrix
  • 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.
amyna
  • amyna
yes, i forgot domain were the x values lol
zepdrix
  • 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|

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zepdrix
  • 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?
amyna
  • amyna
yes, but how should i word my explanation for both?
zepdrix
  • zepdrix
Hmm :d
amyna
  • amyna
ya thats the hard part
zepdrix
  • 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.
zepdrix
  • zepdrix
I dunno, just an idea ^
amyna
  • amyna
alrighty ! i'll come up with something eventually! Thank you! :)
zepdrix
  • zepdrix
:3

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