The function you are asked to graph is $g(x) = 2 \sqrt[3]{x}$, which is the cubic root of $x$, scaled by a factor of 2.

Transformations:

1. Parent Function: The parent function is $f(x) = \sqrt[3]{x}$. Its graph passes through the origin $(0, 0)$, extends into the positive $x$-axis smoothly, and into the negative $x$-axis as a reflection.

2. Vertical Stretch: The function $g(x) = 2 \sqrt[3]{x}$ stretches the graph of $f(x) = \sqrt[3]{x}$ vertically by a factor of 2. This makes the curve rise more steeply in the positive region and descend more steeply in the negative region.

The graph you have provided corresponds to the correct transformation of $g(x)$. The curve starts from the origin and extends both in positive and negative directions as expected from the cubic root function, with a clear vertical stretch evident.

Would you like further details on the function transformations, or have any other questions?

Related Questions:

1. How does a horizontal stretch affect the graph of a function?
2. What happens if you reflect $g(x) = 2 \sqrt[3]{x}$ across the y-axis?
3. How would the graph change if the equation was $g(x) = -2 \sqrt[3]{x}$?
4. What is the domain and range of $g(x) = 2 \sqrt[3]{x}$?
5. How do you differentiate $g(x) = 2 \sqrt[3]{x}$?

Tip:

When applying vertical transformations (like stretches or compressions), only the y-values of points change, not the x-values.