1. **State the problem:** We are given the function $f(x,y) = x^2 y + \cos(x)$ and need to understand or analyze it. 2. **Identify the components:** The function has two variables $x$ and $y$. It consists of a term $x^2 y$ which is a product of $x^2$ and $y$, and a trigonometric term $\cos(x)$ which depends only on $x$. 3. **Formula and rules:** The function is a sum of a polynomial term and a trigonometric term. Important rules: - $x^2 y$ means $x$ squared times $y$. - $\cos(x)$ is the cosine of $x$, which oscillates between $-1$ and $1$. 4. **Intermediate work:** There is no simplification needed as the function is already in simplest form. 5. **Explanation:** This function outputs a value based on inputs $x$ and $y$. The $x^2 y$ term grows quadratically with $x$ and linearly with $y$. The $\cos(x)$ term adds oscillation depending on $x$. Final answer: The function is $f(x,y) = x^2 y + \cos(x)$ as given.