State the interval(s) over which the function  
f
(
x
)
=
x
2
−
5
x
−
2
  is continuous.

The function \( f(x) = x^2 - 5x - 2 \) is a quadratic function, which is a polynomial. Polynomial functions are continuous over their entire domain, which is the set of all real numbers.

Therefore, the function \( f(x) = x^2 - 5x - 2 \) is continuous on the interval:

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

Would you like more details on why polynomial functions are continuous, or do you have any other questions?

Here are 5 related questions to explore further:
1. How do you determine the continuity of a rational function?
2. What are the general characteristics of continuous functions?
3. How do we find intervals of differentiability for a function?
4. What happens to continuity at points where the function is not defined?
5. Can discontinuities occur in polynomial functions?

**Tip:** Polynomial functions are always continuous and differentiable over all real numbers.

State the interval(s) over which the function f(x) = x^2 − 5x − 2 is continuous.

Explore how to determine the interval of continuity for the polynomial function f(x) = x^2 − 5x − 2. This problem covers key concepts in algebra and continuity, showing that polynomial functions are continuous over all real numbers. Suitable for students in Grades 10-12.

Math Problem Statement

State the interval(s) over which the function
f ( x )

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation