marcelie
  • marcelie
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
Mathematics
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katieb
  • katieb
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marcelie
  • marcelie
|dw:1444618045238:dw|
jim_thompson5910
  • jim_thompson5910
where are you stuck?
marcelie
  • marcelie
in range

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jim_thompson5910
  • jim_thompson5910
what is the lowest y can go?
anonymous
  • anonymous
the range for f(x) = 2^-x?
marcelie
  • marcelie
yes
marcelie
  • marcelie
woukd range be (- infinity to infity ) ot 90 to infinity
jim_thompson5910
  • jim_thompson5910
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 \(\LARGE (0, \infty)\)
marcelie
  • marcelie
ohh can the range be 0 ?
jim_thompson5910
  • jim_thompson5910
you mean can 0 be in the range?
anonymous
  • anonymous
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 \[2^{-2}=\frac{ 1 }{ 4}\]
anonymous
  • anonymous
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 "[ , ]"
anonymous
  • anonymous
Because no matter what number you put in for "x" in either function, you will never get the function to equal to zero
marcelie
  • marcelie
oh so mostly ranges are 0 ?
anonymous
  • anonymous
range refers to what values are possible along your y-axis and domain refers to what values are possible along your x-axis
marcelie
  • marcelie
oh
jim_thompson5910
  • jim_thompson5910
the range is a collection of numbers usually. Not just a single number
anonymous
  • anonymous
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 \[(0,\infty)\]
marcelie
  • marcelie
got it :)

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