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

Accepted Solution

Hello!The answer is: [tex]g(x)=-\sqrt[3]{x-1}[/tex]Why?Let's check the roots and the shown point in the graphic (2,-1)First,[tex]0=-\sqrt[3]{x-1}\\\\0^{3}=(-\sqrt[3]{x-1})^{3}\\\\0=-(x-1)\\\\x=1[/tex]then,[tex]g(0)=-\sqrt[3]{0-1}\\g(0)=-(-1)\\g(0)=1\\y=1[/tex]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 ([tex]g(x)=-\sqrt[3]{x-1}[/tex])Second,Evaluating the function at (2,-1)[tex]y=-\sqrt[3]{x-1}\\-1=-\sqrt[3]{2-1}\\-1=-\sqrt[3]{1}\\-1=-(1)\\-1=-1[/tex]-1=-1It means that the function passes through the given point.Hence,The equation which represents g(x) is [tex]g(x)=-\sqrt[3]{x-1}[/tex]Have a nice day!