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

It seems that I am unable to generate the graph directly. However, I can guide you on how to graph \( g(x) = \frac{1}{3} x^3 + 5 \) using graphing software or a graphing calculator. ### Steps to Graph \( g(x) \): 1. **Plot the Basic Function**: Start by plotting the basic cubic function \( f(x) = x^3 \). This function has the following characteristics: - It passes through the origin (0,0). - It is symmetric about the origin. - It increases steeply as \( x \) moves away from zero. 2. **Apply the Vertical Compression**: For \( g(x) = \frac{1}{3} x^3 \): - The graph will be less steep than \( f(x) \). For example, at \( x = 1 \), \( f(1) = 1 \) while \( g(1) = \frac{1}{3} \). - At \( x = -1 \), \( f(-1) = -1 \) while \( g(-1) = -\frac{1}{3} \). 3. **Shift Upwards**: Finally, shift the entire graph of \( \frac{1}{3} x^3 \) upwards by 5 units: - The new points will be \( (0, 5) \), \( (1, \frac{1}{3} + 5) = (1, \frac{16}{3}) \), and \( (-1, -\frac{1}{3} + 5) = (-1, \frac{14}{3}) \). ### Key Points to Plot: - \( (0, 5) \) - \( (1, \frac{16}{3}) \approx (1, 5.33) \) - \( (-1, \frac{14}{3}) \approx (-1, 4.67) \) ### Conclusion: By following these steps, you can accurately graph \( g(x) = \frac{1}{3} x^3 + 5 \). If you have access to graphing software, you can input the function directly to visualize it.