Question

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Answer 1

Option B: $y=-\sqrt[3]{x-4}+7$ is the new equation

Explanation:

The given equation is $y=-\sqrt[3]{x}$

We need to find the new graph which is shifted 7 units up and 4 units right.

First, we shall shift the graph 7 units up.

The general formula to shift the graph b units up is given by

$y=f(x)+b$

Thus, to shift the graph 7 units up, let us substitute $b=7$ and $f(x)=-\sqrt[3]{x}$ in the general formula, we have,

$y= -\sqrt[3]{x} +7$

Now, we shall shift the graph 4 units right.

The general formula to shift the graph b units right is given by

$y=f(x-b)$

Thus, to shift the graph 4 units right, let us substitute $b=4$ and $f(x)= -\sqrt[3]{x}+7$ in the above equation, we have,

$y=-\sqrt[3]{x-4}+7$

Therefore, the new equation is $y=-\sqrt[3]{x-4}+7$

Therefore, Option B is the correct answer.