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Beginning with the graph of f(x)=x^2 what transformations are needed to form g(x) = 1/3(x+3)^2-3

User Matm
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Looking at the functions f(x) and g(x), we can see that, starting with f(x), the value of x was increased by 3, then the function was multiplied by 1/3 and lastly, the function was decreased by 3 units.

An increase of 3 units in the value of x means a horizontal translation of 3 units to the left.

A multiplication of 1/3 means a vertical dilation by a factor of 1/3.

A decrease of 3 units in the value of f(x) means a vertical translation of 3 units down.

User Seidah
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