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
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Online "^" is used to indicate an exponent, e.g., x^2 = x squared.
I need help drawing a picture to represents 3 times 50 equals 150
To determine the end behavior of the graph of a polynomial function, you need to examine the leading term of the function. The leading term is the term with the highest exponent.
In the given polynomial function, the leading term is -3x^5.
To describe the end behavior, we consider the sign and degree of the leading term.
Since the leading term has an odd degree (5), it indicates that the graph will have opposite behavior at the extremes of the x-axis. Specifically, as x approaches negative infinity (or very large negative values), the graph will decrease without bound. On the other hand, as x approaches positive infinity (or very large positive values), the graph will increase without bound.
Therefore, the end behavior can be summarized as follows:
As x approaches negative infinity, the graph of the polynomial will decrease without bound.
As x approaches positive infinity, the graph of the polynomial will increase without bound.
In summary, the end behavior of the graph is that it approaches negative infinity on the left and positive infinity on the right. The leading term is -3x^5.