https://file.aiquickdraw.com/mathbot/file/1726773312994ylxw2f2n.jpg

The function provided is:

\[
f(x) = x^2 - 10x - 5
\]

This is a quadratic function. Since quadratic functions are defined for all real numbers (there are no restrictions like division by zero or square roots of negative numbers), the domain of this function is all real numbers.

In interval notation, the domain is:

\[
(-\infty, \infty)
\]

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How would you find the range of this quadratic function?
2. Can you identify the vertex of the quadratic function?
3. How do you solve for the x-intercepts (if they exist) of this function?
4. How can you determine whether the parabola opens upward or downward?
5. How do transformations affect the domain and range of quadratic functions?

**Tip:** For any polynomial function like this one, the domain is always all real numbers unless explicitly stated otherwise.

Find the domain of the function f(x) = x^2 - 10x - 5.

This guide explains how to find the domain of the quadratic function f(x) = x^2 - 10x - 5. It covers the core mathematical concepts of polynomial functions and shows why the domain is all real numbers. Suitable for students in Grades 8-10.

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