The image shows the mathematical function $f(x) = x^2 + 1$.

This is a simple quadratic function, where the variable $x$ is squared and then incremented by 1. It describes a parabola opening upwards with its vertex at $(0, 1)$, which is the minimum point of the function.

Would you like to analyze this function further or explore specific aspects such as its graph, domain, or range? Let me know if you'd like more details!

Here are some related questions you might find helpful:

1. What is the vertex of the parabola represented by $f(x) = x^2 + 1$?
2. How do you graph the function $f(x) = x^2 + 1$?
3. What is the domain of the function $f(x) = x^2 + 1$?
4. What is the range of the function $f(x) = x^2 + 1$?
5. How can we find the derivative of $f(x) = x^2 + 1$?

Tip: The graph of a quadratic function $ax^2 + bx + c$ always has a U-shape, where the direction of the opening depends on the coefficient $a$. For $a > 0$, it opens upwards, and for $a < 0$, it opens downwards.