Question

If the parent function is \root(3)(x), describe the translation of the function y=\root(3)(x+4)-3

Answer 1

The parent function moves 4 units right and 3 units down. This is a translation by the vector.

According to the question,

Transformation $\sqrt[3]{x}$ maps  onto $\sqrt[3]{x+4} -3$ . Take f(x) =  $\sqrt[3]{x}$ and f(x+4)=$\sqrt[3]{x+4}$.

f(x) =  $\sqrt[3]{x}$

f(x+4)=$\sqrt[3]{x+4}$

f(x+4) - 3=$\sqrt[3]{x+4}$ - 3

Analyze the function to see the translations. f(x-4) corresponds to a horizontal translation 4 units in the positive 'x' direction. f(x)-3 corresponds to a vertical translation 3 units in the negative 'y' direction.

Hence, the parent function moves 4 units right and 3 units down. This is a translation by the vector.

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