Math Problem Statement
Solution
To solve this problem, we need to determine the continuity of the function .
Step-by-Step Solution:
-
Nature of the Function:
The given function is a polynomial. Polynomial functions are continuous everywhere on the real line. -
Polynomial Functions:
For any polynomial function, there are no breaks, jumps, or points of discontinuity. The function is smooth and continuous across all real numbers. -
Conclusion:
Since is a polynomial, it is continuous for all real values of . Therefore, the correct answer is:B. It is continuous for all .
Would you like more details or have any questions about this solution?
Here are 5 related questions for further exploration:
- What are the key properties that make a polynomial function continuous?
- How do you test the continuity of more complex, non-polynomial functions?
- What is the difference between continuity and differentiability in a function?
- Can a function be continuous but not differentiable? If so, how?
- What is the formal definition of continuity at a point?
Tip: When dealing with functions, remember that all polynomials are continuous and differentiable everywhere on their domain, which is the set of all real numbers.
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Math Problem Analysis
Mathematical Concepts
Algebra
Polynomials
Continuity
Formulas
f(x) = x^3 + x + 3
Theorems
Polynomials are continuous for all real numbers.
Suitable Grade Level
Grades 9-12
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