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 November 17th, 2011, 09:01 AM #1 Member   Joined: Aug 2011 Posts: 78 Thanks: 0 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. November 18th, 2011, 04:03 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,370 Thanks: 2007 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. November 18th, 2011, 09:40 AM   #3
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 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. November 18th, 2011, 01:29 PM #4 Global Moderator   Joined: Dec 2006 Posts: 20,370 Thanks: 2007 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. November 21st, 2011, 12:57 AM #5 Member   Joined: Aug 2011 Posts: 78 Thanks: 0 Re: Sketch y=-(x+2)^3 Thanks skipjack I appreciate the help mate  Tags sketch Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post ibrahima Calculus 1 October 9th, 2013 05:47 AM Scientific Calculus 3 October 31st, 2011 06:34 AM kolg Calculus 7 April 10th, 2010 08:21 AM rodjav305 Algebra 9 July 27th, 2009 06:30 PM Soha Algebra 1 December 26th, 2006 03:12 PM

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