Question

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The function g(x) = 3(x − 8)¹ – 5 (x − 8) - 6 is the result of four
transformations on function f(x).
The order of transformations were, 12 units down, 8 units right, and then
scaling down by 1/2. What is the original function?

Answer 1

To find the original function f(x) that was transformed into g(x) = 3(x - 8)¹ − 5 (x - 8) - 6, you need to reverse the given transformations, resulting in scaling up by 2, shifting left by 8 units, and adding 12 to the result.

Step-by-step explanation:

The student asked what the original function f(x) was before the four transformations were applied to obtain

g(x) = 3(x − 8)¹ − 5 (x − 8) - 6.

We need to reverse the transformations mentioned: scaling down by 1/2, translating 8 units to the right, and translating 12 units down, to find the original function.

1. The scaling down by 1/2 suggests the function was scaled by a factor of 2. So we multiply by 2 to undo this: 2g(x).
2. Then, to compensate for the 8 units right translation, we shift the function 8 units to the left by replacing x with x+8.
3. Lastly, to undo the 12 units down, we add 12: f(x+8) + 12.

Therefore, the original function f(x) is obtained by reversing the transformations on g(x), which yields

f(x) = 2(× 3(x − 8) − 5(x − 8) - 6) + 12.