SOLUTION: 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, �le

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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