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$61-72$ Graphing Logarithmic Functions Graph the function,not by plotting points, but by starting from the graphs in Figures4 and $9 .$ State the domain, range, and asymptote.$$g(x)=\log _{6}(x-3)$$
Domain: $(3, \infty)$Range: all real numbersAsymptote: $x=3$
Algebra
Chapter 4
Exponential and Logarithmic Functions
Section 3
Logarithmic Functions
Missouri State University
Oregon State University
McMaster University
University of Michigan - Ann Arbor
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so we know how to graft the being log of X function. Well, we also know that inside the longer than function if we have some X minus K, this means that we're shifting the grab. This means that we're shifting the graph to the right K units to the right K units. And so so in this problem, we have this. We have this X we have this x minus three. And so this means that we're shifting the longer than function to the right three units. And so so, normally, normally we have this Assen tote at X is equal to three. But this is accidents alive. Normally we have this. This vertical Assam choke at X is equal to zero. Sorry X is equal to zero. And so now if we're shifting this to the right, three units will now are vertical. Aston Tote occurs at three and we know that at at X is equal to four. We'll have our Rx interception. So So this is our vertical Lassen tote. And so and so our graph looks something like like this. And so now we confined our domain range and and are asking, what will our domain is from is from positive three to infinity or domain is from positive three to infinity. Our range is from negativity to positivity to positivity. And then our Assen tote are asking Tote occurs at X is equal to three. And so this is This is our solution and and then this is our graph. Remember we we shifted our log our log of X craft to the right to the right, three units.
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