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Write a formula for the function obtained when the graph is shifted as described. Use parentheses in appropriate places.

Write a formula for the function obtained when the graph is shifted as described. Use-example-1

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Given:

The function if given as,


f(x)=x^2\text{ . . . .(1)}

The objective is to write the formula for the transformations.

Step-by-step explanation:

Reflection over the x-axis:

For the first transformation of reflection over the x-axis,


\begin{gathered} f(x)=-f(x) \\ f(x)=-(x^2)\text{. . . . .(2)} \end{gathered}

Shifting 13 units down:

Then, for shifting down 13 units down the equation will be,


f(x)=f(x)-13

Then, the equation (2) can be written as,


f(x)=-(x)^2-13\text{ . . . . (3)}

Shifting 4 units right:

For, shifting 4 units to the right the equation will be,


f(x)=f(x-4)

Then, the equation (3) can be written as,


f(x)=-(x-4)^2-13\text{ }

Hence, the equation of the transformed graph is f(x) = -(x-4)²-13.

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