1. **State the problem:** Classify the function $h(x) = x^3 + 1$ and find its domain. 2. **Identify the type of function:** The function $h(x) = x^3 + 1$ is a sum of a cubic term $x^3$ and a constant 1. 3. **Recall definitions:** - A **polynomial function** is a function of the form $a_nx^n + a_{n-1}x^{n-1} + \cdots + a_1x + a_0$ where $n$ is a non-negative integer and coefficients $a_i$ are real numbers. - A **rational function** is a ratio of two polynomials. - A **root function** involves roots such as square roots, cube roots, etc. 4. **Classify $h(x)$:** Since $h(x)$ is a polynomial of degree 3 (cubic), it is a **polynomial function**. 5. **Find the domain:** Polynomial functions are defined for all real numbers, so the domain is $(-\infty, \infty)$. **Final answer:** - The function $h(x) = x^3 + 1$ is a **polynomial function**. - The domain is $(-\infty, \infty)$.