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!

Explore the graph of y = ln(x) + x^3, covering logarithmic and cubic functions, inflection points, and behavior near zero. Understand how calculus principles apply to analyze the function's shape and properties, suitable for advanced high school or college-level students.

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