The end behavior of a function is the behavior of the graph of the function f(x) as x approaches positive infinity or negative infinity. 2 . End behavior describes where a function is going at the extremes of the x-axis. Cubic functions are functions with a degree of 3 (hence cubic ), which is odd. Khan Academy is a 501(c)(3) nonprofit organization. A horizontal asymptote is a horizontal line such as y = 4 that indicates where a function flattens out as x … Use arrow notation to describe the end behavior and local behavior of the function below. The end behavior of a function is the behavior of the graph of the function f(x) as x approaches positive infinity or negative infinity. End behavior of rational functions Our mission is to provide a free, world-class education to anyone, anywhere. End behavior of polynomial functions helps you to find how the graph of a polynomial function f(x) behaves (i.e) whether function approaches a positive infinity or a negative infinity. End Behavior of Functions The end behavior of a graph describes the far left and the far right portions of the graph. I. Predict the end behavior of the function. Show Solution Notice that the graph is showing a vertical asymptote at [latex]x=2[/latex], which tells us that the function is undefined at [latex]x=2[/latex]. Linear functions and functions with odd degrees have opposite end behaviors. Find the real zeros of the function. This end behavior of graph is determined by the degree and the leading co-efficient of the polynomial function. The end behavior of cubic functions, or any function with an overall odd degree, go in opposite directions. Recall that we call this behavior the end behavior of a function. As we pointed out when discussing quadratic equations, when the leading term of a polynomial function, [latex]{a}_{n}{x}^{n}[/latex], is an even power function, as x increases or decreases without … This function is an odd-degree polynomial, so the ends go off in opposite directions, just like every cubic I've ever graphed. This polynomial is much too large for me to view in the standard screen on my graphing calculator, so either I can waste a lot of time fiddling with WINDOW options, or I can quickly use my knowledge of end behavior.. Steps involved in graphing polynomial functions: 1 . The end behavior of the function with respect to the distance helps to design the roller coaster more efficiently. To sketch any polynomial function, you can start by finding the real zeros of the function and end behavior of the function . Using the leading coefficient and the degree of the polynomial, we can determine the end behaviors of the graph. 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