(3,5) is a point on the graph of y = f(x). Find the corresponding point on the graph of each of the following relations

Question

a) y=3f(-x + 1) + 2

what do I do with the negative sign before the x (-x)?

Answer 1

well, we know that f(3) = 5

That means that if 5 = 3f(-x+1) + 2

then f(-x+1) = 1
Hmmm. If x = -2 then we have

y = 3f(3)+2 = 3(5)+2 = 17

Is there more to this problem than you have stated? Is the graph a line, parabola, what?

We do know that 3f(-x+1)+2 is f(x) reflected about the line x=1, scaled by a factor of 3 and shifted up by 2.

Answer 2

Thanks and no, it doesn't state whether or not its a parabola, etc.

f(3) = 5?

isn't x=3 and y=5?

also, how is f(-x+1) = 1 :S did you factor out the negative?

Answer 3

Hmm. good question. I guess I was rambling around ideas, and lost track of what was what.

I think my only relevant comment is about the reflection, scaling, and translation, and even it was a bit off.

If y=f(x)

y = f(x-1) is the same graph shifted one unit to the right.

f(1-x) is that graph reflected about the line x=1

3f(1-x) is the translated, reflected graph scaled by a factor of 3

3f(1-x)+2 is the translated, reflected, scaled graph, shifted up 3 units.

If we call this new function g(x) = 3f(1-x)+2, then we can't evaluate g(3) becauise that is 3f(-2)+2 and we don't know what f(-2) is.

So, are we supposed to find g(-2)? That would be 3f(3)+2 = 17, so I guess you could say that (-2,17) is a "corresponding point".

Are we supposed to find x so that g(x) = 5? If so, that means that 3f(1-x)+2 = 5 and so 3f(1-x) = 3 and so f(1-x) = 1

But we have no idea where f(x) = 1.

I think hyou need to take a look at your course materials to see what they are trying to get at with this problem.