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haterofmath
Graph the function, not by plotting points, but by starting from the graphs in the figures below. State the domain, range, and asymptote. y = 1 + log3 x
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it is \(y=1+\log_3(x)\) ?
you cannot take the log of a non - positive number, so domain is \[(0,\infty)\]
range of log is all real numbers, so range of \(1+\log_3(x)\) is also all real numbers \(\mathbb{R}\)
there is no horizontal asymptote, but there is a vertical asymptote at \(x=0\) as the function goes to \(-\infty\) as \(x\to 0\)
here is a nice picture, make sure you click on "real valued plot" because wolfram will give you the complex log if you are not careful http://www.wolframalpha.com/input/?i=1%2Blog%28x%29
actually, here is one for \(y=1+\log_3(x)\) http://www.wolframalpha.com/input/?i=1%2Blog_3%28x%29