Answer:
![f(x)=\sqrt[3]{x-2} +1](https://img.qammunity.org/2023/formulas/mathematics/high-school/3g51v1iboi4cprsdtd3poa29usx8gdrpw4.png)
Explanation:
Given function for graph:
![f(x)=1\sqrt[3]{x-h} +k](https://img.qammunity.org/2023/formulas/mathematics/high-school/e89narq4d0lnvs1voadajt77i0kdjb5u8t.png)
where (h, k) is the midpoint of the curve.
Therefore, the parent function is
![f(x)=\sqrt[3]{x}](https://img.qammunity.org/2023/formulas/mathematics/high-school/bpa3vuuo5dtqkg0vqcw69omticpmu0m3k9.png)
can be obtained by translating
to
units to the right and
units up
The x and y intercept of
is the origin
Therefore, this graph has been translated 2 units to the right and 1 unit up.
Therefore,
and

Substituting these values into the given function:
![\implies f(x)=\sqrt[3]{x-2} +1](https://img.qammunity.org/2023/formulas/mathematics/high-school/xkws2a76x0jkgq20rpli2hoh8h7jfm5waf.png)