Question

The point Q($\frac{\pi}{2}$, 4) lies on the function f(x). Suppose f(x) is transformed according to y = -$\frac{1}{2}$f[0.2(x+6)] - 15. Determine the transformed point, Q'. Enter only the x- coordinate, a single value, rounded to 2 decimal places (ie. 2.56 or 7.00 or 1.40)

          The point Q($\frac{\pi}{2}$, 4) lies on the function f(x). Suppose f(x) is transformed according to
y = -$\frac{1}{2}$f[0.2(x+6)] - 15. Determine the transformed point, Q'. Enter only the x-
coordinate, a single value, rounded to 2 decimal places (ie. 2.56 or 7.00 or 1.40)
        
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The point Q((π)/(2), 4) lies on the function f(x). Suppose f(x) is transformed according to
y = -(1)/(2)f[0.2(x+6)] - 15. Determine the transformed point, Q'. Enter only the x-
coordinate, a single value, rounded to 2 decimal places (ie. 2.56 or 7.00 or 1.40)

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Precalculus with Limits
Precalculus with Limits
Ron Larson 2nd Edition
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The point Q (, 4) lies on the function f(x). Suppose f(x) is transformed according to y = - f[0.2(x+6)] - 15. Determine the transformed point, Q'. Enter only the x-coordinate, a single value, rounded to 2 decimal places (i.e. 2.56 or 7.00 or 1.40).
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Transcript

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00:01 So in this question, we're given a point q, which is the point pi over 2, comma, 6, and this point lies on the function f of x.
00:09 And we're going to be given a transformation of that function f of x.
00:15 They say we have y equals negative a half times f of 0 .9 times the quantity of x plus 20 minus 16.
00:24 And we want to figure out the x coordinate of the transform point q prime so what's the idea here well if i ever have something that is of the form y equals a times f of the quantity of b times x minus c plus d what affects my x my x my x is affected by my b and my c so my a and my d this affects the y my a and my d my d they affect the y whereas the b and the c they affect the x now we always do our b transformation first okay so we started with an x coordinate this time of pi over two.
01:34 Now, how do i get my new x after my b value? well, it turns out that you take your initial x, pi over two, and you divide it by that b value.
01:50 So you divide it by 0 .9.
01:53 If you went to a calculator and you took pi over two and you divided that by point nine you would get 1 .75 so i'm rounding to two decimal places here because that's what they're saying to do in my answer 1 .75.
02:09 All right...
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