# Thread: Transformations- graphing a logarithm

1. ## Transformations- graphing a logarithm

Hey everyone,

So I am doing a lesson on transformations... And the 'textbook' I am using, or lack thereof, that comes with my math correspondence unit is a little short on examples, so I am having trouble with this problem.

It is a simple question.

Graph y= -2 Log3(x-3)- 1

So, on the graph, this will mean a stretch factor of 2, which gives me (1,0), (3,2), and (9,4)... Now I do the rest and get (4,-1), (6,-3), and (12,-5)... (keeping in mind that I flipped on the x-axis)

Now the only thing that is really confusing me is: at -3 there is an asymptote because we moved 3 to the right.. But for my graph on my graphing calculator, there is randomly another sort of asymptote when y= 3 as well? Basically the line comes from the 4th quadrant, into the 2nd, and stops at (3,3). There is one example in the book that has the same thing, but no explanation.. I am wondering if anyone can explain this to me?

2. Originally Posted by Slipery
Hey everyone,

So I am doing a lesson on transformations... And the 'textbook' I am using, or lack thereof, that comes with my math correspondence unit is a little short on examples, so I am having trouble with this problem.

It is a simple question.

Graph y= -2 Log3(x-3)- 1

So, on the graph, this will mean a stretch factor of 2, which gives me (1,0), (3,2), and (9,4)... Now I do the rest and get (4,-1), (6,-3), and (12,-5)... (keeping in mind that I flipped on the x-axis)

Now the only thing that is really confusing me is: at -3 there is an asymptote because we moved 3 to the right.. But for my graph on my graphing calculator, there is randomly another sort of asymptote when y= 3 as well? Basically the line comes from the 4th quadrant, into the 2nd, and stops at (3,3). There is one example in the book that has the same thing, but no explanation.. I am wondering if anyone can explain this to me?
1. The start point is the basic function: $\displaystyle y = \log_3(x)$

2. Dilating by the factor 2: $\displaystyle y = 2 \log_3(x)$

3. Reflecting over the x-axis: $\displaystyle y = -2 \log_3(x)$

4. Translating by 3 units to the right: $\displaystyle y = -2 \log_3(x-3)$

5. Translating by 1 unit down: $\displaystyle y = -2 \log_3(x-3)-1$

EDIT: I've attached a drawing to demonstrate the transformations: It starts with the dark blue graph and it ends with the red graph.

3. Wow, thank you very much for doing all that work.. Is there any way that you could give me the link to that website or program you used to make the graph?

4. Originally Posted by Slipery
Wow, thank you very much for doing all that work.. Is there any way that you could give me the link to that website or program you used to make the graph?
Of course. Have a look here:

Graph

The program is freeware.