Question

The function represented by graph B is g(x) = _________

The function represented by graph C is h(x) = _________

Answer 1

`g(x)=\sqrt[3]{x-1}`

`h(x)=\sqrt[3]{x}-1`

Explanation:

Graph represents the parent function

`f(x)=\sqrt[3]{x}`

The translation is defined as

`g(x)=f(x+a)+b`

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

From the the given graph it is clear that graph A shifts 1 unit right to get the graph B. So, a=-1, b=0.

`g(x)=\sqrt[3]{x-1}`

From the the given graph it is clear that graph A shifts 1 unit down to get the graph C. So, a=0, b=-1.

`h(x)=\sqrt[3]{x}-1`

Therefore, the required functions are
`g(x)=\sqrt[3]{x-1}` and
`h(x)=\sqrt[3]{x}-1`.