The domain of a function refers to all the possible input values (usually \(x\)-values) for which the function is defined.

For the function \( f(x) = -2x^2 - 3 \):

1. The function is a quadratic function, which is a polynomial. Polynomial functions are defined for all real numbers.

2. There are no restrictions like division by zero or taking the square root of a negative number that would limit the domain.

Therefore, the domain of \( f(x) = -2x^2 - 3 \) is all real numbers.

In interval notation, the domain is:
\[
(-\infty, \infty)
\]

Would you like more details or have any other questions? Here are 5 related questions:

1. What is the range of the function \( f(x) = -2x^2 - 3 \)?
2. How do you determine the domain of a rational function?
3. What are the key characteristics of quadratic functions?
4. How does the leading coefficient of a quadratic function affect its graph?
5. Can a quadratic function have a restricted domain? If so, under what conditions?

**Tip:** For any polynomial function, the domain is always all real numbers unless otherwise restricted by the context of the problem.

Explore the domain of the function -2x^2 - 3, which is all real numbers. Learn about quadratic functions and their domains with a detailed explanation and interval notation. Suitable for high school students.

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