Question

The graph of g(x) is a reflection and translation of ∛x see attachment, please help

Answer 1

Hello!

The answer is: $g(x)=-\sqrt[3]{x-1}$

Why?

Let's check the roots and the shown point in the graphic (2,-1)

First,

$0=-\sqrt[3]{x-1}\\\\0^{3}=(-\sqrt[3]{x-1})^{3}\\\\0=-(x-1)\\\\x=1$

then,

$g(0)=-\sqrt[3]{0-1}\\g(0)=-(-1)\\g(0)=1\\y=1$

So,  we know that the function intercepts the axis at (1,0) and (0,1), meaning that the function match with the last given option

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

Second,

Evaluating the function at (2,-1)

$y=-\sqrt[3]{x-1}\\-1=-\sqrt[3]{2-1}\\-1=-\sqrt[3]{1}\\-1=-(1)\\-1=-1$

-1=-1

It means that the function passes through the given point.

Hence,

The equation which represents g(x) is $g(x)=-\sqrt[3]{x-1}$

Have a nice day!