	Determine the values of x for which the function is continuous. If the function is not continuous, determine the reason.

f(x) =   100  -   x 2


The given function is:

\[
f(x) = 100 - x^2
\]

This is a quadratic function, which is a type of polynomial. Polynomials are continuous for all real values of \(x\) because they are defined everywhere and have no breaks, jumps, or points of discontinuity.

### Continuity of \( f(x) \):
- Since \(f(x) = 100 - x^2\) is a polynomial, it is continuous for all real numbers.
- There are no points where the function is undefined, and thus, the function is continuous on the entire real number line.

### Conclusion:
The function \(f(x) = 100 - x^2\) is continuous for all values of \(x \in (-\infty, \infty)\).

Would you like a more detailed explanation of continuity in functions? Here are some questions to expand on this topic:

1. What is the general definition of continuity for a function?
2. How do we determine if a piecewise function is continuous?
3. What are the common types of discontinuities in functions?
4. How can we check the continuity of rational functions?
5. What are some real-life applications of continuous functions?

**Tip:** Polynomial functions are always continuous over their entire domain.

Determine the values of x for which the function is continuous. If the function is not continuous, determine the reason.

f(x) = 100 - x^2

Explore how to determine the continuity of the polynomial function f(x) = 100 - x^2. Learn key algebraic concepts such as polynomial continuity, and see why this function is continuous for all real numbers. Ideal for students in Grades 10-12.

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