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marcelie

  • one year ago

Help please !!!! For the following exercises, graph the transformation of f (x) = 2^x. Give the horizontal asymptote, the domain, and the range. f(x) = 2^-x

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  1. marcelie
    • one year ago
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    |dw:1444618045238:dw|

  2. jim_thompson5910
    • one year ago
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    where are you stuck?

  3. marcelie
    • one year ago
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    in range

  4. jim_thompson5910
    • one year ago
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    what is the lowest y can go?

  5. anonymous
    • one year ago
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    the range for f(x) = 2^-x?

  6. marcelie
    • one year ago
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    yes

  7. marcelie
    • one year ago
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    woukd range be (- infinity to infity ) ot 90 to infinity

  8. jim_thompson5910
    • one year ago
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    on your graph notice how y slowly approaches the x axis. It doesn't actually reach the x axis. So y = 0 is the lowest y can go which means the range is \(\LARGE (0, \infty)\)

  9. marcelie
    • one year ago
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    ohh can the range be 0 ?

  10. jim_thompson5910
    • one year ago
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    you mean can 0 be in the range?

  11. anonymous
    • one year ago
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    You can also look back on how exponents work. Despite the negative sign in front of the exponent, all that means is that you'll get the inverse of what you would've gotten if that had been a positive exponent. ie.) \[2^{2}=4\] while \[2^{-2}=\frac{ 1 }{ 4}\]

  12. anonymous
    • one year ago
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    It would approach 0 but it would never actually touch 0, which is why it's left in the open parenthesis "( , )" instead of the closed parenthesis "[ , ]"

  13. anonymous
    • one year ago
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    Because no matter what number you put in for "x" in either function, you will never get the function to equal to zero

  14. marcelie
    • one year ago
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    oh so mostly ranges are 0 ?

  15. anonymous
    • one year ago
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    range refers to what values are possible along your y-axis and domain refers to what values are possible along your x-axis

  16. marcelie
    • one year ago
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    oh

  17. jim_thompson5910
    • one year ago
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    the range is a collection of numbers usually. Not just a single number

  18. anonymous
    • one year ago
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    So going back to the funcitons... For both functions, you know that your "x" variable can be all real numbers so your domain for both functions would be \[(-\infty,\infty)\]. And you always want to make sure that you put \["\infty"\] in an open parenthesis. As for range, you know that you'll get only positive values for both functions (because of how exponents work, as I've explained above) and it'll only approach zero but never touch the line, so the ranges for both functions would be \[(0,\infty)\]

  19. marcelie
    • one year ago
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    got it :)

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