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Question:

In the function $8465_w185_h21.png$ , a and b are both integer constants and b is positive. If the end behavior of the graph of y = f(x) is positive for both very large negative values of x and very large positive values of x, what is true about a and b?

A a is positive, and b is odd.
Explaination

A polynomial function of even degree with a positive leading coefficient will have positive end behavior for both very large negative values of x and very large positive values of x. For a polynomial function in the form $6450_w203_h22.png$ to be of even degree with a positive leading coefficient, a must be positive and b must be odd.