Question

determine the intervals on which the following function is continuous. p(x) = 6x⁵ + 3x² + 1 the function is continuous on the interval(s) (simplify your answer. type your answer in interval notation. use a comma to separate answers as needed )

Explanation:

Step1: Identify the function type

The function \( p(x) = 6x^5 + 3x^2 + 1 \) is a polynomial function.

Step2: Recall continuity of polynomials

Polynomial functions are continuous everywhere on the real number line. The real number line in interval notation is \( (-\infty, \infty) \).

Answer:

\((-\infty, \infty)\)