#2 Choose the end behavior of the graph of the polynomial function.
f(x) 3x^3+3x^2-6x-5. I got Falls to the left and rises to the right. Is this correct? Thanks
Yes. End behavior is determined by the sign of the x^3 term, which dominates for very large |x|
To determine the end behavior of the graph of a polynomial function, we need to look at the leading term of the polynomial.
In this case, the leading term is 3x^3. The degree of the polynomial is the highest power of x that appears, which is 3 in this case.
Since the degree of the polynomial is odd (3 is an odd number), we know that the graph will have opposite end behavior. That means if the polynomial falls to the left, it will also fall to the right, or if it rises to the left, it will also rise to the right.
To determine whether the graph falls or rises, we look at the coefficient of the leading term. In this case, the coefficient is positive (3 is positive), so the graph will rise as x approaches negative infinity and rise as x approaches positive infinity.
Therefore, your answer of "Falls to the left and rises to the right" is incorrect. The correct end behavior of the graph of the polynomial function f(x) = 3x^3 + 3x^2 - 6x - 5 is "Rises to the left and rises to the right".