Answer:
Write a function based on the given parent function and the transformations in the given order.
1 answer:
Given the function
![y= \sqrt[3]{x}](https://tex.z-dn.net/?f=y%3D%20%5Csqrt%5B3%5D%7Bx%7D%20)
A s<span>hift 9 units to the left will result in the function:
</span><span>![y'= \sqrt[3]{x+9}](https://tex.z-dn.net/?f=y%27%3D%20%5Csqrt%5B3%5D%7Bx%2B9%7D%20)
</span>A <span>Shrink horizontally by a factor of 5 will result in the function:
![y''=\sqrt[3]{5(x+9)}](https://tex.z-dn.net/?f=y%27%27%3D%5Csqrt%5B3%5D%7B5%28x%2B9%29%7D)
A </span>r<span>eflection across the x-axis will result in the function
![y'''=-\sqrt[3]{5(x+9)}](https://tex.z-dn.net/?f=y%27%27%27%3D-%5Csqrt%5B3%5D%7B5%28x%2B9%29%7D)
Therefore, the final function after the series of transformation is
</span><span></span>
A s<span>hift 9 units to the left will result in the function:
</span><span>
</span>A <span>Shrink horizontally by a factor of 5 will result in the function:
A </span>r<span>eflection across the x-axis will result in the function
Therefore, the final function after the series of transformation is
</span><span>
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All the points that are 6 units from (-1, 1) are those on the circle
(x+1)^2 +(y-1)^2 = 36
For y=0, the two points of interest satisfy
(x+1)^2 +1 = 36
(x+1)^2 = 35 . . . . . . subtract 1
x+1 = ±√35
x = -1±√35
The points you seek are (-1-√35, 0) and (-1+√35, 0), about (-6.916, 0) and (4.916, 0).
(x+1)^2 +(y-1)^2 = 36
For y=0, the two points of interest satisfy
(x+1)^2 +1 = 36
(x+1)^2 = 35 . . . . . . subtract 1
x+1 = ±√35
x = -1±√35
The points you seek are (-1-√35, 0) and (-1+√35, 0), about (-6.916, 0) and (4.916, 0).