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 4 from the [math: y] -axis - a translation of [math: π2] \frac{ \pi }{2} units in the positive direction of the [math: x] -axis- a translation of 1 unit in the positive direction of the [math: y] -axisThe equation of the image is given by:

选项
A.A. [math: y=sin(14(x−π2))+1] y=sin( \frac{1}{4} (x- \frac{ \pi }{2} ))+1
B.B. [math: y=4sin((x−π2))+1] y=4sin( (x- \frac{ \pi }{2} ))+1
C.C. [math: y=sin(12(x+π2))−1] y=sin( \frac{1}{2} (x+ \frac{ \pi }{2} ))-1
D.D. [math: y=4sin((x+π2))−1] y=4sin( (x+ \frac{ \pi }{2} ))-1
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标准答案
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思路分析
We begin by restating the problem to ensure clarity: a graph of y = sin(x) undergoes three transformations in sequence: a dilation of factor 4 from the y-axis, a translation of π/2 units to the right along the x-axis, and a translation of 1 unit upward along the y-axis. We must determine the equation of the image. Option A: y = sin(14(x − π/2)) + 1 - This option shows a horizontal compression inside the sine by a factor of 14 because the argument is 14 times (x − π/2). Such a large horizontal scaling is not consistent with the desc......Login to view full explanation

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