Why is the asymptote shifted and points don't match?

[Matt1234]

Here is what the graph looks like on a graphing calculator (notice the equation at the top):

http://img62.imageshack.us/img62/8898/graphingcalc.jpg


Here is what my graph looks like:

http://img53.imageshack.us/img53/7475/lastscanc.jpg

I don't understand why the asymptote is shifted 6 units left instead of 3 units left, And the point on my graph don't seem quite right.

i have the points (-1, -3)
Yet the graphing calculator has (-1, -3.79)

Note : where i wrote original points I am referring to y = log x


I don't see what i hsve done wrong, can someone help me.

Thanks.

 

[Mark44]

Your first step should have taken care of the compressions/expansions, so you should have looked at y = 2ln(1/2*x) first. The 1/2*x inside the parentheses causes an expansion away from the vertical axis. After that, take care of reflections, and finally translations.

 

[Matt1234]

thanks will try that

 

[Mark44]

Notice that y = -2log(.5x + 3) + 3 = -2log(.5(x + 6)) - 3. This means that
1. The domain of this function is {x | x > -6}
2. The graph of y = -2log(.5x) has been translated to the left by 6 units, and down by 3 units.

 

[Matt1234]

You hit the nail on the head my friend, I forgot to factor Stupid me!

 

[Matt1234]

ill try again and post back my result

 

[Matt1234]

Got it thank you very much, forgot to factor.

Here it is:
http://img62.imageshack.us/img62/2599/lastscanjy.jpg