Question

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

Answer 1

Answer:

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

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

Step-by-step 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 $h(x)=\sqrt[3]{x}-1$.