anonymous
  • anonymous
find the domain and range of each function f(x)=log3x D:_________ R:_________ V.A_________ (V.A stand for vertical asymptote)
Mathematics
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jamiebookeater
  • jamiebookeater
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helder_edwin
  • helder_edwin
any type of logarithm works only for positive numbers so \[ \large 3x>0\Rightarrow x>0/3=0 \] so the domain is \((0,+\infty)\)
anonymous
  • anonymous
For the domain, you will be able to determine its value by considering that your base is positive.
helder_edwin
  • helder_edwin
the logarithm of a number can be positive or negative so the range is \(\mathbb{R}\)

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helder_edwin
  • helder_edwin
a logarithmic function has a vertical asymptote when its argument is zero. so \[ \large 3x=0\Rightarrow x=0/3=0 \] therefore VA: x=0

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