Des

Yasir Ali

Yasir Ali

Answered question

2022-04-13

Des

Answer & Explanation

user_27qwe

user_27qwe

Skilled2023-04-27Added 375 answers

To obtain the function y=(1113x+9)215 from y=x4, we need to apply a series of transformations. Let's break it down step by step:
First, we apply a horizontal compression or shrink by a factor of 1311 to y=x4. The general formula for a horizontal compression or stretch of a function y=f(x) is given by y=f(xa), where a is the compression/stretch factor. In this case, we have:
y=(x1311)4=(1113x)4=1464128561x4
So the function y=x4 is horizontally compressed by a factor of 1311 to obtain y=1464128561x4.
Next, we apply a reflection about the x-axis to the compressed function 1464128561x4. This reflection can be obtained by multiplying the function by 1. So we have:
y=1464128561x4
Now, we need to apply a vertical stretch by a factor of 15 to the reflected function. The general formula for a vertical compression/stretch of a function y=f(x) is given by y=af(x), where a is the compression/stretch factor. In this case, we have:
y=15(1464128561x4)=219615190407x4
Finally, we apply a vertical translation or shift downward by 15 units to the vertically stretched function. The general formula for a vertical translation of a function y=f(x) is given by y=f(x)+k, where k is the vertical shift. In this case, we have:
y=219615190407x415
Therefore, the function y=(1113x+9)215 is obtained from y=x4 by applying a horizontal compression by a factor of 1311

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