Question

cubic and cube root functions and equations
the function $f(x) = \sqrt3{x}$ is reflected over the x-axis to create the graph of $g(x) = -\sqrt3{x}$.
which is the graph of $g(x)$?

Explanation:

Step1: Recall parent function shape

The parent function $f(x)=\sqrt[3]{x}$ has a graph that increases from the lower left to the upper right, passing through the origin.

Step2: Apply reflection rule

A reflection over the x-axis transforms $f(x)$ to $g(x)=-f(x)$. This means every y-value of the parent function is multiplied by $-1$, flipping the graph vertically. So the increasing curve of $f(x)$ becomes a decreasing curve, where as $x$ increases, $g(x)$ decreases, matching the second graph.

Answer:

The second graph from the top (the one where the curve goes from the upper left to the lower right, decreasing across the plane)