## Inverted Transformation? if (8, -5) on graph of f(x), then

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
jolie3000
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### Inverted Transformation? if (8, -5) on graph of f(x), then

I have spent about 2 hours trying to wrap my head around a question and I have found 4 different ways with 4 different answers on how to solve it? Can anyone help me? The question is:

The point (8,-5) is on the graph of y=f(x), which point must be on the graph of y=1/f(-x)-2

TIA for any guidance

stapel_eliz
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The point (8,-5) is on the graph of y=f(x), which point must be on the graph of y=1/f(-x)-2
To learn, in general, about function transformations and translations, try here.

I will guess that "1/f(-x)-2" means the following:

. . . . .$\frac{1}{f(-x)}\, -\, 2$

Also, I will guess that the "which point" language is referring to some list of point from which you are to choose...?

Since x = 8 is an input in f(x), then probably they've given you a point with x = -8, since -x = -(-8) = +8, which is the x-value they gave you to start with.

Since f(8) = -5, then f(-(-8)) will also equal -5. Then 1/f(-(-8)) will equal 1/(-5) = -1/5. Then subtract the 2 to find the y-value for (1/f(-x)) - 2. See if this matches any of the options they gave you.

Thank you!

jolie3000
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Joined: Sat Apr 18, 2009 10:13 pm
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### Re: Inverted Transformation? if (8, -5) on graph of f(x), then

Hi,
I wish they gave me options, that would have helped. There are no options, no graphs, and no coordinates to choose from or use. The question above is exactly how it's written
Also yes it is written with the 1 over the function, only the -2 is below the line. I have tried inputting 8,-5 into the equation and then flipping and solving for y, which got me 8,1/3. I tried doing the reciprocal then reflecting on the y-axis, then the translation..............I'm at aloss on this one.

stapel_eliz
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If the expression is as follows:

. . . . .$\frac{1}{f(-x)\, -\, 2}$

...then try doing what was demonstrated previously. You know that (x, y) = (8, -5) is on the graph of f(x), so you know that f(8) = -5. Since this is all you know, then try plugging x = -8 into the expression they've given you, and simplifying to find the corresponding value of y.

jolie3000
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Joined: Sat Apr 18, 2009 10:13 pm
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### Re: Inverted Transformation? if (8, -5) on graph of f(x), then

So do I simplify and flip the x & y because it's inverted? Or would I just simply simplify?

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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I'm sorry, but I don't know what you mean by "flipping the x and the y"...?

Instead, try using what they've given you. You've been given that f(8) = 5. You're asked about an expression involving f(-x). Try plugging "-8" in for "x" in the expression they've given you:

. . . . .f(-x) = f(-[-8]) = f(8)

Plug the value they give you for f(8) into the given expression. Then simplify to find the resulting value.