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# How to find y=-2f(x) Watch

1. The coordinates for y=f(x) are

(-2, 0)
( 2,-3)
( 6, 0)

How can I draw y = -2f(x)
2. Treat f(x) as if it were just a number.
3. This is just an expansion of the graph in the y direction i.e
Multiply each of your y-coordinates by -2

So there is no change to (-2,0) and (6,0) but (2,-3) goes to (2,6).
4. (Original post by forgottensecret)
This is just an expansion of the graph in the y direction i.e
Multiply each of your y-coordinates by -2

So there is no change to (-2,0) and (6,0) but (2,-3) goes to (2,6).
So the -2 only effects the y coordinates?
5. (Original post by Tempa)
So the -2 only effects the y coordinates?
Yeah if it's not in the brackets than y is affected but not x. In the brackets x is affected but not y
6. y = -2f(x)

A stretch in the y direction by scale factor -2

(-2, 0) ---> (-2,0)
( 2,-3)----> (2,6)
( 6, 0)----> (6,0)
7. Essentially what's happening is that you are flipping the graph in the x axis (y=0) then stretching it parallel to the y axis by a scale factor of two. We aren't moving sideways in any way so we can just multiply the y co-ordinates by -2.
8. (Original post by Tempa)
The coordinates for y=f(x) are

(-2, 0)
( 2,-3)
( 6, 0)

How can I draw y = -2f(x)
I always thought functions were written as f(x)=y or f(x)= -2y. All it means is when x equals a certain value, y is going to equal another. So just substitute the given values:

1) f(-2)=0 becomes f(-2)=-2 x 0, you take the x and y value and get (-2,0)
2) f(2)=-3 becomes f(2)= -2 x -3 and you get (-2, -3)
3) f(6)=0 becomes f(g)= -2 x 0 and you get (6,0)

x value remains constant because the only number being multiplied is the y value, but if you were given a second equation of f(-2x)=y, than the y would b constant and x would change. All depends on the equatuion.

then you plot you points and get your lines. You will find that the graph was stretched and fliped so that now instead of having a slope of 1, the slope is -2 and your y intercept should still be 0

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Updated: December 20, 2010
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