Question 116021: Describe the transformations on the following graph of f(x)=log(x).
State the placement of the vertical asymptote and x-intercept after the transformation. For example, “left 1” or “stretched vertically by a factor of 2” are descriptions.
b) g(x)=-log(x)
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! b)
Description of transformation:
Remember,  is the same as y. So this means 
Now if we negate both sides to get 
So  is simply making each y coordinate becomes it's opposite. So something like (0,2) becomes (0,-2) and (3,-2) becomes (3,2), etc
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Answer:
So what's happening is that the graph is being reflected over the x-axis
Notice if we graph and , we get
 Graph of  (red) and  (green)
and we can visually verify the transformation
Vertical Asymptote:
From the graph, we can see that the vertical asymptote is  . Since the transformation reflected the graph across the x-axis, the vertical asymptote of is the same as the vertical asymptote of
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Answer:
So the vertical asymptote of is
We can verify this by looking at the graph above
x-intercept in (x, y) form:
From the graph, we can see that the x-intercept of is (1,0). Since we've reflected everything with respect to the x-axis, the point on the x-axis is not affected. In other words the x-intercept of is the same as the x-intercept of
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Answer:
So the x-intercept of is (1,0)
Once again, we can visually verify this if we look at the graph above
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