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Write the new function f(x) that satisfies the following conditions: y =/x/ is reflected with respect...

Write the new function f(x) that satisfies the following conditions: y =/x/ is reflected with respect to the x-axis, compressed by a factor of 1/3 , shifted to the left three units, and up five units.

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Answer #1

Lets start with .

To reflect with respect with the -axis we need to multiply by so that .

Next we compress by multiplying the previous expression by . The result is .

To shift a function three units to the right, we need to evaluate at instead of . So, we get .

Finally, to shift the graph five units up, we add a the constant term and get .

The function is defined by .

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