Final answer:
The end behavior of the polynomial function p(x) = 4x³ + 6x² + 16x + 24 is that as x approaches negative infinity, p(x) approaches negative infinity, and as x approaches positive infinity, p(x) approaches positive infinity.
Step-by-step explanation:
The end behavior of a polynomial function can be determined by examining the leading term of the function. In the given polynomial function, p(x) = 4x³ + 6x² + 16x + 24, the leading term is 4x³. The degree of the polynomial function is 3 (since the exponent of the leading term is 3), and the coefficient of the leading term is positive (4).
When the degree of a polynomial function is odd and the coefficient of the leading term is positive, the end behavior of the function is as follows:
- As x approaches negative infinity, the function approaches negative infinity.
- As x approaches positive infinity, the function approaches positive infinity.
Therefore, in this case, as x approaches negative infinity, p(x) approaches negative infinity, and as x approaches positive infinity, p(x) approaches positive infinity.