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3 years ago

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

Mathematics

1 answer:

svetoff [14.1K]3 years ago

5 0

<h2>Hello!</h2>

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

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!

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