graphing transformations

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flyingfreedom

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[attachment=0:3cm79vjp]ScreenHunter_01 Jan. 21 13.33.gif[/attachment:3cm79vjp]

The answer is (0, -12), but I don't understand how to get there.
I tried reflecting the point 6 in the y-axis then expanding by 3 giving me -18 I then added the phase shift which brings me to -24. So I get (-24,-12). Obviously I've gone wrong somewhere, but I can't seem to find where. Can someone help me please. :shock:
 

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flyingfreedom said:
[attachment=0:15iokgr3]ScreenHunter_01 Jan. 21 13.33.gif[/attachment:15iokgr3]

The answer is (0, -12), but I don't understand how to get there.
I tried reflecting the point 6 in the y-axis then expanding by 3 giving me -18 I then added the phase shift which brings me to -24. So I get (-24,-12). Obviously I've gone wrong somewhere, but I can't seem to find where. Can someone help me please. :shock:
Click to expand...

You know the value of f(6) = -12<<< you'll need to convert the new x[sub:15iokgr3]1[/sub:15iokgr3]

now

-1/3 * x[sub:15iokgr3]1[/sub:15iokgr3] + 6 = 6

x[sub:15iokgr3]1[/sub:15iokgr3] = 0

there is no shift in 'y' - so the point (0,-12) will be on the new graph.

Anyway, I have to admit that without knowing the answer, it would have taken a loooong time for me to see this reasoning and come to the answer.
 
I am not sure if there is any better method but this is how I would do it:
Since we do not know the exact function, I would first look to get y as -12 and x as 6 (ditto what is given)
y = -12 for all the options.

So I would look how to get 6 with (-1/3)x+6

Therefore I would have (-1/3)x+6 = 6 which means x = 0. Hence option (C)
 
Hello all! Thanks for the answers.
Unfortunately I still don't understand. Why do you try to get 6 with (-1/3)x+6?
 
from my logic (which I guess isn't right here) I would try to get Y(-12). That would give me (-1/3)x+6=-12 so x = 54.

Just to show you the way I'm thinking so you can hopefully get me thinking right!
 
Never mind, once more in my logic:
1st thing to understand is that f(x) and f((-1/3)x+6) are the same function. They just denote different points on the same graph.

All we know is -12 = f(6) (given)
Compare this with y = f((-1/3)x+6) and you have y = -12 and (-1/3)x+6 = 6

Hope this helps.
 
This is not any particular method that we have used. Its just the concept of functions that is put to use.
If you are not clear of the idea of functions and want to start on from there then start from sets and relations between them.
 
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