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November 17th, 2011, 09:01 AM   #1
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Sketch y=-(x+2)^3

Hey there,
To the following problem:
x = -2 coordinates (-2,0)
y = -8 coordinates (0,-8)

Would you say the curve -(x+2)^3 is a reflection in the x-axis of the curve y=x^2?

Thanks

Last edited by skipjack; November 5th, 2014 at 09:31 AM.
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November 18th, 2011, 04:03 AM   #2
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No. It's the reflection in the x-axis of the curve y = (x + 2)³.

Last edited by skipjack; November 5th, 2014 at 09:31 AM.
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November 18th, 2011, 09:40 AM   #3
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Re:

Quote:
Originally Posted by skipjack
No. It's the reflection in the x-axis of the curve y = (x + 2)³.
Thanks skipjack! As stupid as it sounds, I'm having difficulty of understanding the translations of cubic graphs. I understand the inflexion but when it comes to understanding horizontal, vertical and reflections. Is it sufficient enough to say that for example so so equation is a translation of +2 in the x-axis of the curve y=x^3 or so?

Do you know of any material on it to help? Thanks again. I understand the process but the different translations I find hard to grasp. Silly as it sounds.

Last edited by skipjack; December 8th, 2014 at 12:18 AM.
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November 18th, 2011, 01:29 PM   #4
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Translations and reflections are easy to do for any curve y = f(x), whether cubic or not.

I'll assume the positive x direction is to the right and the positive y direction is up. Just reference the list of new equations, and read the effect accomplished in comparison with the original curve y = f(x).

1. y = f(x + c) $\ \,\,$Translated left by distance c.
2. y = f(x - c) $\,\,\ $Translated right by distance c.
3. y = f(x) + c $\,\,\,$Translated up by distance c.
4. y = f(x) - c $\ \,\,$Translated down by distance c.
5. y = -f(x) $\ \ \,\,\,\ \ \ $Reflected in the x-axis.
6. y = f(-x) $\ \ \,\,\,\ \ \ $Reflected in the y-axis.
7. y = 2c - f(x) $\,$Reflected in the line y = c.
8. y = f(2c - x) $\,$Reflected in the line x = c.
9. x = f(y) $\ \ \ \,\,\ \ \ \ $Reflected in the line y = x.
10. x = -f(-y) $\ \ \,\,$Reflected in the line y = -x.

If you have a graphing calculator, try some of the above for the cubic graph of y = x³ - 3x + 2 and let us know how you get on.

Last edited by skipjack; November 5th, 2014 at 09:50 AM.
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November 21st, 2011, 12:57 AM   #5
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Re: Sketch y=-(x+2)^3

Thanks skipjack I appreciate the help mate
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