Option B: [tex]$y=-\sqrt[3]{x-4}+7$[/tex] is the new equation
Explanation:
The given equation is [tex]$y=-\sqrt[3]{x}$[/tex]
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
[tex]y=f(x)+b[/tex]
Thus, to shift the graph 7 units up, let us substitute [tex]b=7[/tex] and [tex]f(x)=-\sqrt[3]{x}[/tex] in the general formula, we have,
[tex]y=$-\sqrt[3]{x}$+7[/tex]
Now, we shall shift the graph 4 units right.
The general formula to shift the graph b units right is given by
[tex]y=f(x-b)[/tex]
Thus, to shift the graph 4 units right, let us substitute [tex]b=4[/tex] and [tex]f(x)=$-\sqrt[3]{x}+7$[/tex] in the above equation, we have,
[tex]$y=-\sqrt[3]{x-4}+7$[/tex]
Therefore, the new equation is [tex]$y=-\sqrt[3]{x-4}+7$[/tex]
Therefore, Option B is the correct answer.
