Determine the continuity of the function 𝑓𝑥=𝑥3-𝑥Question 7Answera.(0, 0)b.(-∞, ∞)c.(0, ∞)d.(-∞, 0)
Question
Determine the continuity of the function
Question 7
Answer
- a. (0, 0)
- b. (-∞, ∞)
- c. (0, ∞)
- d. (-∞, 0)
Solution
To determine the continuity of the function , we can follow these steps:
1. Break Down the Problem
We need to analyze the function to check if it is continuous over its entire domain or particular intervals. A function is continuous if it is defined and does not have any breaks, holes, or asymptotes.
2. Relevant Concepts
A polynomial function is continuous everywhere on the real number line. The function is a polynomial function, so we can conclude its continuity based on this property.
3. Analysis and Detail
The function is a polynomial of degree three. Since all polynomial functions are continuous across their entire domain, we can assert:
- Domain of : The function is defined for all (from to ).
- Continuity: There are no breaks or discontinuities in the function since it is a polynomial.
4. Verify and Summarize
Since is a polynomial, it is continuous for all .
Final Answer
The function is continuous on the interval . Therefore, the correct answer is: b. (-∞, ∞)
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