\( \begin{array}{l}\text { Describe how the graph of } g(x)=\frac{1}{3} x^{3}+5 \text { can be obtained from the } g r a p h ~ o f ~\end{array}(x)=x^{3} \). Then graph the function \( g(x) \).

To obtain the graph of \( g(x) = \frac{1}{3} x^{3} + 5 \) from the graph of \( f(x) = x^3 \), you can start by vertically stretching the original cubic function \( f(x) \) by a factor of \( \frac{1}{3} \) and then shifting the entire graph upward by 5 units. This means the steepness of \( f(x) \) will be reduced, producing a wider curve, and placing all points of the graph 5 units higher on the vertical axis. Graphing \( g(x) \) would show a cubic curve that starts from the lower left, gradually curls through the origin point at (0, 5), and rises through the upper right. The inflection point remains at the origin due to the nature of cubic equations, maintaining the characteristic "S" shape of cubic functions but wider and shifted up. So, the critical features are preserved, just adjusted in scale and position!