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April 5th, 2014, 07:01 PM   #1
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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?
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April 5th, 2014, 07:50 PM   #2
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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 07:56 PM.
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April 5th, 2014, 07:56 PM   #3
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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, 08:11 PM   #4
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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 $x=9$.
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April 5th, 2014, 08:18 PM   #5
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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.
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April 5th, 2014, 08:32 PM   #6
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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).
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April 6th, 2014, 06:17 AM   #7
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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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