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Write a rational function f(x) = 1/x that has been transformed in the following ways

1. Translated 6 units down
2. Translated 5 units to the right
3. Translated 4 units up, and 3 units to the right
4. Translated 6 units left, 2 units down
5. Translated 1 unit right, 5 units up, and reflected across the x-axis
6. Translated 3 units up, 2 units left, and reflected across the x-axis

User JRI
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Answer:

Explanation:

Translated 6 units down:

To translate the function 6 units down, we need to subtract 6 from the original function. So the transformed function is:

f(x) = 1/x - 6

Translated 5 units to the right:

To translate the function 5 units to the right, we need to replace x with (x-5) in the original function. So the transformed function is:

f(x) = 1/(x-5)

Translated 4 units up, and 3 units to the right:

To translate the function 4 units up and 3 units to the right, we need to replace x with (x-3) and add 4 to the original function. So the transformed function is:

f(x) = 1/(x-3) + 4

Translated 6 units left, 2 units down:

To translate the function 6 units left and 2 units down, we need to replace x with (x+6) and subtract 2 from the original function. So the transformed function is:

f(x) = 1/(x+6) - 2

Translated 1 unit right, 5 units up, and reflected across the x-axis:

To translate the function 1 unit right and 5 units up, we need to replace x with (x-1) and add 5 to the original function. To reflect across the x-axis, we need to negate the entire function. So the transformed function is:

f(x) = -1/(x-1) + 5

Translated 3 units up, 2 units left, and reflected across the x-axis:

To translate the function 3 units up and 2 units left, we need to replace x with (x+2) and add 3 to the original function. To reflect across the x-axis, we need to negate the entire function. So the transformed function is:

f(x) = -1/(x+2) + 3

User Jstaab
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