End Behavior refers to the behavior of a graph as it approaches either negative infinity, or positive infinity. Answer: The end behavior of a function f describes the behavior of the graph of the function at the "ends" of the x-axis. Though a polynomial typically has infinite end behavior, a look at the polynomial can tell you what kind of infinite end behavior it has. Determining end behavior from the equation. The degree and leading coefficient of a polynomial always explain the end behavior of its graph: 1. Even and Positive: Rises to … For polynomials that have an even degree, the ends go in the same direction (like a quadratic). 1. Determine which way the ends of the graph point. In other words, the end behavior of a function describes the trend of the graph if we look to the right end of the x-axis (as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ). Identify the degree of the function. This end behavior of graph is determined by the degree and the leading co-efficient of the polynomial function. f(x) = 2x 3 - x + 5 Use the degree of the function, as well as the sign of the leading coefficient to determine the behavior. A close look at polynomials shows a wide variety of interesting behavior. 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. We'll review that below. Example 8: Given the polynomial function a) use the Leading Coefficient Test to determine the graph’s end behavior, b) find the x-intercepts (or zeros) and state whether the graph crosses the x-axis or touches the x-axis and turns around at each x-intercept, c) find the y-intercept, d) determine the symmetry of the graph, e) indicate the maximum possible turning points, and f) graph. The degree and the sign of the leading coefficient (positive or negative) of a polynomial determines the behavior of the ends for the graph. 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. Show Instructions In general, you can skip the multiplication sign, so `5x` is equivalent to `5*x`. Indeed when the range is maximized there seem to be only four different graphs:Up up: highest nonzero power is even with a positive coefficient.Down down: highest nonzero power is even with a negative coefficient.Up down: high; The Degree of a Polynomial with one variable is the largest exponent of that variable. Answer: The end behavior of a function f describes the behavior of the graph of the function at the "ends" of the x-axis. Play this game to review Algebra II. To determine its end behavior, look at the leading term of the polynomial function. polynomial long division, or inﬁnite limits and sketch the horizontal or slant asymptote. Identify the degree of the function. To determine its end behavior, look at the leading term of the polynomial function. Never more than the Degree minus 1. End Behavior of a Polynomial. Knowing the degree of a polynomial function is useful in helping us predict its end behavior. Let's think about its end behavior, and we could think about it relative to a second degree polynomial. Explanation: 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. For us to determine the end behavior of a polynomial, we first have to know two important characteristics: degree and leading coefficient. Recall that we call this behavior the end behavior of a function. 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