My Math Forum Transformation of Graphs
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 April 5th, 2014, 08:01 PM #1 Member   Joined: Nov 2013 Posts: 47 Thanks: 4 Transformation of Graphs Okay, maybe there's something that I'm missing here, but isn't the graph y=abs(x) shifted right 3 units, stretched by a factor of 3, shifted vertically down 2 units, and reflected across the x-axis not equal to y=-3abs(x-3) -2?
 April 5th, 2014, 08:50 PM #2 Senior Member     Joined: Apr 2014 From: Greater London, England, UK Posts: 320 Thanks: 155 Math Focus: Abstract algebra It would be $\displaystyle y=-|x-9|+2$. Original graph: $\displaystyle y\,=\,|x|$ Shift right 3 units: $\displaystyle y\,=\,|x-3|$ Stretched by factor 3: $\displaystyle y\,=\,3\left|\frac x3 -3\right|\,=\,|x-9|$ (NB: When a graph $\displaystyle y=f(x)$ is stretched by a factor $\displaystyle k\ne0$, the equation fo the new graph is $\displaystyle y=kf\left(\frac xk\right)$. You were thinking $\displaystyle y=kf(x)$ – that would be stretching it in the $y$-direction only, not $x$.) Down 2 units: $\displaystyle y\,=\,|x-9|-2$ Reflect in $x$-axis: $\displaystyle y\,=\,-|x-9|+2$ Last edited by Olinguito; April 5th, 2014 at 08:56 PM.
April 5th, 2014, 08:56 PM   #3
Member

Joined: Nov 2013

Posts: 47
Thanks: 4

Perhaps I'm still missing it, but I can't match that to any of the answer choices...
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 April 5th, 2014, 09:11 PM #4 Senior Member     Joined: Apr 2014 From: Greater London, England, UK Posts: 320 Thanks: 155 Math Focus: Abstract algebra I would say there was something wrong with the question and/or answers. The sequence of transformations maps the origin $(0,0)$ to $(9,2)$. None of the answers gives $y=2$ when you substitute $x=9$.
 April 5th, 2014, 09:18 PM #5 Member   Joined: Nov 2013 Posts: 47 Thanks: 4 According to the professor's answer key, the answer is A: -(3abs(x-3) -2) But that answer doesn't make sense.. Strange. Maybe there is something wrong with this question.
 April 5th, 2014, 09:32 PM #6 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,557 Thanks: 2558 Math Focus: Mainly analysis and algebra Well, if "stretched" is take to mean in the $y$ direction, I'd agree. When you reflect in the $x$-axis the turning point should move from (9,-2) to (9,2).
 April 6th, 2014, 07:17 AM #7 Global Moderator   Joined: Dec 2006 Posts: 20,098 Thanks: 1905 Strictly speaking, the question should specify the stretch properly, including the direction and the fixed point. The fixed point is commonly assumed to be the origin. A stretch in both the x and y directions (i.e., in all directions) from the origin is usually described as a magnification (or there's a precise technical term that I forget for the moment). Thanks from Olinguito

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