CONFUSING math II question

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<p>So I was studying Transformation and symmetry in Barrons when I encountered this question:
Which of the following is a transformation of y=f(x) that translates this function down 3, shrinks it horizontally by a factor of 2, and reflects it about the x-axis?
C. y= -f(1/2x) -3
D. y= -f(2x) -3
Answer: D, but here's the confusing part, according to the definition: "y= f(ax) shrinks (stretches) f(x) horizontally by a factor of |1/a| if |a|>1 (|a|<1)". Then I applied to the question: shrinks by a factor of 2 => 2 = 1/a => a= 1/2 => should be C. But then It would be illogical if C is the answer because |a| = |1/2| <1 => should be STRETCH according to the definition.....
Any ideas?? </p>

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<p>I actually got y = -f(2x) + 3.</p>

<p>The definition you provided is confusing and may not even be the correct usage of “shrink” as we know it. Given f(x), then for a > 0, f(ax) stretches the graph horizontally by a factor of 1/a, or shrinks the graph by a factor of a (this is the way I would word it). For example, if you have f(x) = sin x, then f(10x) = sin 10x has a wavelength that is 10 times less, and we’d likely say that the graph of f(x) is “shrunk” horizontally by a factor of 10.</p>

<p>Back to the question, f(x) translates to f(x) - 3. If you shrink f(x) - 3 horizontally by a factor of 2, you should obtain f(2x) - 3. But if you reflect y = f(2x) - 3 about the x-axis, you will get y = -f(2x) + 3, not y = -f(2x) - 3.</p>

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<p>my definition is from barrons SAT math II, can u write down the full definition you found in your book?
mine are:
+) y = af(x) stretches (shrinks) f(x) vertically by a factor of |a| if |a| >1 (|a|<1)
+) y = f(ax) shrinks (stretches) f(x) horizontally by a factor of |1/a| if |a| >1 (|a|<1)
are these two correct? if not then can you correct them for me?</p>

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<p>@Sparkkid1234‌ the explanation given by @MITer94‌ is correct
y = -f(2x) + 3</p>

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<p>I suggest you use some simple examples e.g. make a simple graph of </p>

<p>y = x</p>

<p>(and y = x - 3)</p>

<p>and</p>

<p>y = x squared</p>

<p>and try their transformations on these two functions (graphing them again). It should be more obvious to see that way and shouldn’t take long.</p>

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<p>@2018RiceParent‌ may I ask if my definitions taken from Barrons correct?</p>

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<p>@Sparkkid1234 see my previous post for the definition I’m currently aware of. This is based on my knowledge of what the words “shrink” and “stretch” mean. For example, if we have f(x), then f(4x) is the same as f, shrunken by a factor of 4. However I don’t see these words too much in math literature since the definitions can be unclear.</p>

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<p>@MITer94‌ thank you. I have another question that i dont quite understand
If x is an angle in quadrant III and tan(x-30) = cot x, x is:

  1. 240
  2. 60</p>
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<ol>
<li>240
60 isn’t in quadrant 3…</li>
</ol>

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<p>@guineagirl96‌ wow, forgot that simple rule… another question, in which quadrant is -60? and why? </p>

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<p>-60 is quadrant 4. </p>

<p>Quad 1 is between 0-90 or -270 to -360
Quad 2 is between 90-180 or -180 to -270
Quad 3 is between 180-270 or -90 to -180
Quad 4 is between 270-360 or (-)0 to -90</p>

<p>negative numbers are just the reverse of positive numbers because its like subtracting from 360.</p>

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<p>Quadrant 4. See this diagram</p>

<p><a href=“Marlene's Blog | Web Corner with Art”>Marlene's Blog | Web Corner with Art;

<p>-60 = 360 - 60 or the same as 300 degrees. The quadrants go counterclockwise (Quadrant I is 0 to 90, II = 90-180, III = 180-270 while finally IV is 270 to 360)</p>