Final answer:
The end behavior of the polynomial function p(x) = -5x^6 - 3x^5 + 4x^2 + 6x is that it tends toward negative infinity as x approaches both positive and negative infinity, due to the leading term being -5x^6.
Step-by-step explanation:
The student has asked about the end behavior of the polynomial function p(x) = -5x^6 - 3x^5 + 4x^2 + 6x.
The end behavior of a polynomial function is determined by the leading term, which is the term with the highest exponent in the polynomial.
Since the leading term here is -5x^6, we know this is a degree 6 polynomial with a negative coefficient.
For large positive values of x (as x approaches positive infinity), the function p(x) will head towards negative infinity, because the leading term has a negative coefficient and an even power, for large negative values of x (as x approaches negative infinity), the function will also head towards negative infinity for the same reason.
Therefore, the end behavior of this polynomial function on both ends is that it tends toward negative infinity.