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**RickyOswaldIOW****Member**- Registered: 2005-11-18
- Posts: 212

I am having a little trouble with scaling curves, for example:

y = -2x^3

I know that;

y = af(x) is scaled in the y direction by a

y = f(ax) is scaled in the x direction by 1/a

So how can I tell if y = -2x^3 is y = -2f(x) or f(-2x)???

Aloha Nui means Goodbye.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

y = -2(x)^3 or y = (-2x)^3?

y = -2(x)^3:

Draw the sketch x^3, then flip it over the y axis. Now stretch it upwards by a factor of two. Plotting some points also helps. For example, plot x = -2, 1, 0, 1, 2, then connect the dots keeping in mind it should look something like x^3.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**RickyOswaldIOW****Member**- Registered: 2005-11-18
- Posts: 212

I know that the curve is exactly the same but if you are asked to describe the transformation, should I say that it's scaled in the y-direction by a factor -2 or in the x-direction by factor -1/2?

Aloha Nui means Goodbye.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Separate the - from the 2. You flip because of the negative, you strech/shirk because of the 2.

But remember that streching the y by a factor of 2 is exactly the same as shrinking the x by a factor of 2, which is exactly the same as streching the x by a factor of 1/2.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**RickyOswaldIOW****Member**- Registered: 2005-11-18
- Posts: 212

So I wont have any questions in the format y = -2x^3 asking in which axis I need to scale?

FYI. The correct term for streching or shrinking the curve is to "scale" it by a "factor"

Aloha Nui means Goodbye.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Right, but "scale" it by a "factor" may not make sense to someone who doesn't know that's the correct term for streching/shrinking

And you probably will have questions like this, but there are just multiple correct answers. Just like if I asked you to give me two numbers when added together that give me 9.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**RickyOswaldIOW****Member**- Registered: 2005-11-18
- Posts: 212

Ah good point!!! I'll write both answers

Aloha Nui means Goodbye.

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,319

Compare y=f(ax[sub]2[/sub]) and y=f(x)

when the two y equals, usually the value in the bracket equals.

ax[sub]2[/sub]=x

thus x[sub]2[/sub]=x/a

**X'(y-Xβ)=0**

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**RickyOswaldIOW****Member**- Registered: 2005-11-18
- Posts: 212

-2x² - 7x + 15

-2[x² + 7/2x] + 15

-2[(x + 7/4)² - 49/16] + 15

-2(x + 7/4)² + 18 + 1/16

Sketch the curve of -2x² - 7x + 15:

2(x + 7/4)² = 18 + 1/16

(x + 7/4)² = 9 + 1/32

x + 7/4 = ±√9 + 1/32

x = - 7/4 ±√9 + 1/32

So the curve would cross the x-axis at -4.76 and +1.26 which, as you already know, is wrong!.

Aloha Nui means Goodbye.

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,319

Yes, but a trick will solve the controversy

devide the original curve or function into such pieces that in each piece x and y are one by one, use my procedure seperately and then stick the pieces by original sequence.

**X'(y-Xβ)=0**

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