Math Problem Statement
For which values of x is the function f(x)equals=3 x cubed+x+1 continuous?
Solution
The function is a polynomial function. Polynomial functions are continuous for all real values of . This is because polynomials are built from basic operations (addition, subtraction, multiplication, and exponentiation) that are continuous everywhere.
Thus, the function is continuous for all real values of , i.e., .
Would you like further details on the continuity of polynomial functions?
Here are 5 related questions to further explore this concept:
- What makes a function discontinuous?
- How do you determine if a rational function is continuous?
- Are all polynomial functions continuous over their entire domain?
- How does the derivative of a polynomial behave with respect to continuity?
- What are some real-world applications of continuous polynomial functions?
Tip: A function is continuous if you can draw its graph without lifting your pen from the paper!
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Math Problem Analysis
Mathematical Concepts
Calculus
Continuity
Polynomial Functions
Formulas
f(x) = 3x^3 + x + 1
Theorems
Continuity of Polynomial Functions
Suitable Grade Level
Grades 11-12