Question 637132: Graph the function: g(x) = 2/3 log_2(x-3) + 2
Plot two points and the asymptotes (if any) of the graph of the function.
Help please! Thank you very much! Can anyone please walk me through the steps to achieve this answer?!
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website!
Graph the function: g(x) = 2/3 log_2(x-3) + 2
Plot two points and the asymptotes (if any) of the graph of the function.
I don't have the means to graph it for you, but I can describe how to do it.
**
start with the basic log curve: y=logx (base 10)
like all logx curves, regardless of base, they have the y-axis is an asymptote, and x-intercept=1.
So this basic curve starts from (0,-∞), crosses the x-axis at 1 and gradually increases to ∞.
..
For given log curve: g(x) = 2/3 log_2(x-3) + 2
Since it is a lower base(2), the curve is above the basic curve when <1, and below the basic curve when x>1.There is no change to the y-axis asymptote or x-intercept at 1.
The 2/3 multiplier stretches the curve, making it more negative below the x-axis and more positive above the x-axis.
(x-3) moves the asymptote and x-intercept 3 units to the right at x=3 and x=4 respectively
Finally, +2 bumps the entire curve 2 units up
..
note:If you have a graphing calculator, it could greatly help you follow the steps above
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