Question

Please help!!!! what is the equation for this graph

Answer 1

`f(x)=\sqrt[3]{x-2} +1`

Explanation:

Given function for graph:
`f(x)=1\sqrt[3]{x-h} +k`

where (h, k) is the midpoint of the curve.

Therefore, the parent function is
`f(x)=\sqrt[3]{x}`

`f(x)=1\sqrt[3]{x-h} +k` can be obtained by translating
`f(x)=\sqrt[3]{x}` to
`h` units to the right and
`k` units up

The x and y intercept of
`f(x)=\sqrt[3]{x}` is the origin

Therefore, this graph has been translated 2 units to the right and 1 unit up.

Therefore,
`h=2` and
`k=1`

Substituting these values into the given function:

`\implies f(x)=\sqrt[3]{x-2} +1`