Suppose that the graph of f contains the point (5,2). Find a point that must be on the graph of g(x)=3f(x+7).
How do I solve this?

Question

anonymous · Answer

I know I gotta plug things in but I am not getting the correct answer so I must be doing it wrong.

hero · Answer

Yeah, there's something I don't like about this

anonymous · Answer

We just started doing these today in class and the teacher confused the crap outta me like usual.

hero · Answer

Are you doing derivatives?

anonymous · Answer

no?

hero · Answer

What is the topic of study?

anonymous · Answer

Transformations

hero · Answer

Okay

hero · Answer

Yeah, I have no clue. I'd have to look up some resources to figure it out

anonymous · Answer

Thanks for trying anyways...

hero · Answer

I don't see how I'm supposed to know what f(12) means

anonymous · Answer

f(12)? where did u get that?

hero · Answer

g(5) = 3f(5 + 7)

anonymous · Answer

ok nevermind

anonymous · Answer

f contains (5,2) that means 
$$f(5)=2$$

hero · Answer

I know that already. It wants f(5+7)

hero · Answer

Any ideas?

anonymous · Answer

no it doesn't ask for that. it says 
"Find a point that must be on the graph of g(x)=3f(x+7)."

hero · Answer

So....what?

anonymous · Answer

so  the only thing you know is that 
$$f(5)=2$$ 
so if 
$$x+7=5$$ then 
$$x=-2$$ so 
$$g(-2)=3f(-2+7)=3f(5)=3\times 2=6$$ so the only thing you know is that (-2,6) is on the graph of g

hero · Answer

Hmm. I think if I would have kept going with my original idea, I would have gotten that

anonymous · Answer

That is correct

hero · Answer

Actually, I wouldn't have. I would have gotten 2,6

anonymous · Answer

Thanks for trying/solving... might need some more help in a sec