horizontal stretch/compression?

werter23

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Sep 23, 2017
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My frined and I had a test and afterwards we were debating whether the following question should've had a k value of 2 or 1/2?
the question stated that y=√x was translated in the following way: vertical compression by factor of 1/3, reflection along x-axis, translation left 3 and down 4, and a horizontal stretch by a factor of 1/2. Now I said the equation was f(x)=-1/3√2(x+3) -4 but my friend replaced the 2 with 1/2. Who would be right in this situation? I'm still a bit foggy with the whole k-value thing. Thanks
 
Neither are correct, actually. All of the translations up to "...and down 4" are correct. At that point, the function would be: f(x) = -1/3√(x+3) - 4. From here, your solution, corrected to include very important grouping symbols, f(x) = -1/3√[2(x+3)] - 4, is incorrect, as is your friend's solution.

In the proper solution, the horizontal stretch constant (you picked k, so we'll go with that) is attached solely to the x, and nothing else. So it would be f(x) = -1/3√(kx+3) - 4. But, now with these few corrections out of the way, the main crux of your question remains - is k equal to 1/2 or 2? Well, to answer that, we need to return to the basics and review the definition of a horizontal stretch/compression. If you can't find this information in your class notes, you might try this pagehttps://cobbk12.blackboard.com/bbcs...ionsShiftsStretchesCompressionsSymmetry2.html, which says: "If |k| < 1 (a fraction between 0 and 1), then the graph is stretched horizontally by a factor of k units. If |k| > 1, then the graph is compressed horizontally by a factor of k units."

According to your post, we want "a horizontal stretch by a factor of 1/2." Since stretches and compressions are inverses, we know that a stretch by a factor of 1/2 is the same as a compression by a factor of 2. The quoted portion of the linked page tells us that, to get a compression of a factor of k, we need a k greater than 1. Hence, k must be 2.
 
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