Here is the graph of the function $y = \ln(x) + x^3$. As you can see, it incorporates both the logarithmic and cubic behavior, with a steep rise for large positive values of $x$ due to the cubic term, and a sharp dip near $x = 0$ due to the logarithmic term.

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Here are 5 questions related to this function:

1. What is the domain and range of $y = \ln(x) + x^3$?
2. How does the function behave as $x \to 0^+$?
3. Where does the function have inflection points?
4. How can we approximate roots of this function numerically?
5. What happens to $y = \ln(x) + x^3$ for negative $x$?

Tip: The natural logarithm $\ln(x)$ is only defined for $x > 0$, so always consider domain restrictions carefully when analyzing logarithmic functions!