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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

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  1. zepdrix
    • one year ago
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    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
    • one year ago
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    yes, i forgot domain were the x values lol

  3. zepdrix
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    yes, but how should i word my explanation for both?

  6. zepdrix
    • one year ago
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    Hmm :d

  7. amyna
    • one year ago
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    ya thats the hard part

  8. zepdrix
    • one year ago
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    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
    • one year ago
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    I dunno, just an idea ^

  10. amyna
    • one year ago
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    alrighty ! i'll come up with something eventually! Thank you! :)

  11. zepdrix
    • one year ago
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    :3

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