Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term.
-3x5 + 9x4 + 5x3 + 3
end behaviour is negative large for positive x. I don't know what you mean by "leading" term.
To determine the end behavior of a polynomial function, we need to examine the leading term of the polynomial and its degree. The leading term is the term with the highest exponent.
In the given polynomial, the leading term is -3x^5, which has a degree of 5. The degree corresponds to the highest power of x in the polynomial.
The end behavior of a polynomial depends on the sign of the leading coefficient (the coefficient of the leading term) and whether the degree of the polynomial is even or odd.
In this case, the leading coefficient is -3. Since the degree is odd (5), the end behavior of the graph will be different for positive values of x and negative values of x. Here's how we can describe the end behavior:
1. As x approaches positive infinity (x → +∞), the leading term -(3x^5) will tend towards negative infinity (-∞), and therefore the graph will decrease without bound.
2. As x approaches negative infinity (x → -∞), the leading term -(3x^5) will tend towards positive infinity (+∞), and thus the graph will increase without bound.
So, the end behavior of the graph of the given polynomial is a decreasing function as x approaches positive infinity and an increasing function as x approaches negative infinity.
The leading term of the polynomial is -3x^5.