The function $f(x) = x^2$ is defined for $x \geq -1$. Since the function is a simple quadratic function with a domain restriction, we can evaluate and discuss its properties:

1. Domain: The function is defined for all $x$ such that $x \geq -1$.

2. Range: Since $f(x) = x^2$ and the smallest value $x$ can take is $-1$, the smallest value of $f(x)$ is $(-1)^2 = 1$. Therefore, the range of the function is $[1, \infty)$.

3. Behavior: The function is increasing for $x > 0$ and decreasing for $x < 0$ in the domain $x \geq -1$.

4. Vertex: The vertex of the parabola is at $x = 0$, where $f(0) = 0^2 = 0$, but this point is not within the domain of the restricted function, so it does not impact the defined range.

5. Graph: The graph is a portion of the parabola $y = x^2$, starting at the point $(-1, 1)$ and extending indefinitely to the right.

If you want details, have any questions, or need a graphical representation, let me know!

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Here are five related questions to consider:

1. What is the derivative of $f(x) = x^2$ for $x \geq -1$?
2. How would the function change if the domain were $x \leq -1$ instead?
3. What is the inverse of the function $f(x) = x^2$ over its defined domain?
4. How do you find the area under the curve $f(x) = x^2$ from $x = -1$ to $x = 2$?
5. What are the roots of the function if the domain were unrestricted?

Tip: For functions with restricted domains, always check how the restriction affects the range and other properties.