题目
题目
单项选择题

A graph of the function with equation [math: y=sin(x)] is transformed by- a dilation of factor 2 from the [math: y] -axis - a translation of [math: π3] \frac{ \pi }{3} units in the negative direction of the [math: x] -axis- a translation of 1 unit in the negative direction of the [math: y] -axisThe equation of the image is given by:

选项
A.A. [math: y=2sin((x+π3))+1] y=2sin( (x+ \frac{ \pi }{3} ))+1
B.B. [math: y=2sin((x+π3))−1] y=2sin( (x+ \frac{ \pi }{3} ))-1
C.C. [math: y=sin(12(x−π3))−1] y=sin( \frac{1}{2} (x- \frac{ \pi }{3} ))-1
D.D. [math: y=sin(12(x+π3))−1] y=sin( \frac{1}{2} (x+ \frac{ \pi }{3} ))-1
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标准答案
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思路分析
We start by clearly restating the problem and the available options to ensure we follow the intended transformations correctly. Question and options restated: - The original graph is y = sin(x). - Transformations applied: (1) a dilation of factor 2 from the y-axis, (2) a translation left by π/3, (3) a translation downward by 1 unit. - The answer choices are: A. y = 2 sin((x + π/3)) + 1 B. y = 2 sin((x + π/3)) − 1 C. y = sin(1/2 (x − π/3)) − 1 D. y = sin(1/2 (x + π/3)) − 1 Option-by-option analysis: Option A: y = 2 sin((x + π/3)) + 1 - This option applies a vertical stretch by a factor of 2 (which matches the dilation b......Login to view full explanation

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