anonymous
  • anonymous
Graph y=log 3(x+2)-1. Then, find the domain/range
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
what does "solve" mean in this context?
anonymous
  • anonymous
Whoops! Not solve. Just graph and find the domain/range
jim_thompson5910
  • jim_thompson5910
I would use a graphing calculator like desmos https://www.desmos.com/calculator to graph this out. You will have to use the change of base formula to make sure the expression is typed in properly you will have to type in log(x+2)/log(3) - 1

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anonymous
  • anonymous
Ok thanks :) Would the domain be all real numbers?
jim_thompson5910
  • jim_thompson5910
why all real numbers?
jim_thompson5910
  • jim_thompson5910
you should have this graph https://www.desmos.com/calculator/fs1pnhr9hx
jim_thompson5910
  • jim_thompson5910
the left side of the graph seems to hit a "wall" of some sort
anonymous
  • anonymous
Ok, now I do. And it does seem like that
jim_thompson5910
  • jim_thompson5910
it turns out that you cannot plug in 0 or negative numbers into a log function so x+2 has to be positive x+2 > 0 leads to x > ???
anonymous
  • anonymous
x=-2 ? x+2=0
jim_thompson5910
  • jim_thompson5910
yeah x = -2 is your vertical asymptote. The graph does NOT touch the vertical asymptote. It only gets closer and closer and closer.
jim_thompson5910
  • jim_thompson5910
solving x+2 > 0 for x gives x > -2, which is the domain
anonymous
  • anonymous
Alright, I see :) Now what about the range?
jim_thompson5910
  • jim_thompson5910
the left side shoots off to negative infinity (very quickly) the right side slowly approaches positive infinity. it just keeps growing forever
anonymous
  • anonymous
so the range would be all real #'s or infinity
jim_thompson5910
  • jim_thompson5910
all real numbers I think you're thinking of this notation \(\Large (-\infty,\infty)\)
anonymous
  • anonymous
Yes :)
anonymous
  • anonymous
Thanks!
jim_thompson5910
  • jim_thompson5910
you're welcome

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