We need to know about cube-root function and reflection to solve this problem. The function is f(x)=[tex]-\sqrt[3]{x-4}[/tex]
A cube-root function is the inverse of a cubic function, a cubic function can be given by f(x)=[tex]x^{3}[/tex], the inverse of this is a cube-root function which can be given by f(x)=[tex]\sqrt[3]{x}[/tex] with vertex at (0,0). The general formula for a cube root function is given be
f(x)=a[tex]\sqrt[3]{x-h} +k[/tex] where a is the measure of how horizontally compressed the graph is and (h,k) is the vertex of the graph. In the question we have to find a cube root function which has been reflected about the y-axis, which means our a will be negative. The vertex of the graph is at (4,0) so (h,k) is (4,0). Thus the cube root function we need is
f(x)=-[tex]\sqrt[3]{x-4}[/tex]
Therefore we found the cube root function that has been reflected about y-axis and the vertex at (4,0) to be f(x)=[tex]-\sqrt[3]{x-4}[/tex]
Learn more about cube root function here:
https://brainly.com/question/15818396
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