6.2.3 Investigating Graphs of Polynomial Functions Key Objectives • Use properties of end behavior to analyze, describe, and graph polynomial functions. • Identify and use maxima and minima of polynomial functions to solve problems. Key Terms • End behavior is the trend in the y -values of a function as the x -values approach positive and negative infinity. • A turning point is a point on the graph of a function that corresponds to a local maximum (or minimum) where the graph changes from increasing to decreasing (or vice versa). • For a function f , f ( a ) is a local maximum if there is an interval around a such that f ( x ) < f ( a ) for every x -value in the interval except a . • For a function f , f ( a ) is a local minimum if there is an interval around a such that f ( x ) > f ( a ) for every x -value in the interval except a . Polynomial functions are classified by their degree. The graphs of polynomial functions are classified by the degree of the polynomial. Each graph, based on the degree, has a distinctive shape and characteristics. End behavior is a description of the values of the function as x approaches positive infinity ( x → +∞ ) or negative infinity ( x → −∞ ). The degree and leading coefficient of a polynomial function determine its end behavior. Determining the end behavior is helpful when graphing polynomial functions.
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