(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
a) y=3f(-x + 1) + 2
what do I do with the negative sign before the x (-x)?
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.
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?
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.
Oh, that negative sign is just trying to be different! It's a rebel in the world of math. So when you see "-x", it means we are taking the opposite of "x". In other words, it's like turning the sign of "x" upside down! It's a bit like asking "Hey 'x', why don't you go the other way?"
So, in this case, we have "-x + 1". To get the corresponding point, you simply substitute "-x + 1" for "x" in the original function. Let's do some math magic!
For the point (3, 5), if we substitute "-x + 1" for "x" in y = f(x), it becomes y = f(-x + 1). Then, we can multiply by 3 and add 2 to get y = 3f(-x + 1) + 2.
So, the corresponding point on the graph of y = 3f(-x + 1) + 2 would be:
(-(-3) + 1, 3(5) + 2)
Simplifying, it would be:
(4, 17)
Tada! You found the corresponding point!
To find the corresponding point on the graph of the relation y = 3f(-x + 1) + 2, you need to substitute the x-coordinate of the given point (3, 5) into the expression for x in the equation -x + 1.
In this case, the expression -x + 1 has the negative sign before the x. This means that you have to substitute the opposite of the x-coordinate of the given point into the expression.
So, substitute -3 for x in the equation:
y = 3f(-(-3) + 1) + 2
Simplifying the expression inside the parentheses:
y = 3f(3 + 1) + 2
Now, you have -x + 1, which simplifies to -(-3) + 1 = 3 + 1 = 4.
Substituting 4 for x in the equation:
y = 3f(4) + 2
Finally, you have the equation in the form y = 3f(x) + 2, where x = 4. The corresponding point on the graph of y = 3f(x) + 2 can be found by evaluating f(4) using the given point (3, 5).