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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 xaxis not equal to y=3abs(x3) 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 $\displaystyle y=x9+2$. Original graph: $\displaystyle y\,=\,x$ Shift right 3 units: $\displaystyle y\,=\,x3$ Stretched by factor 3: $\displaystyle y\,=\,3\left\frac x3 3\right\,=\,x9$ (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: $\displaystyle y\,=\,x92$ Reflect in $x$axis: $\displaystyle y\,=\,x9+2$ 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...

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(x3) 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).


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