P.F.IF.A

Analyze functions using different representations.

P.F.IF.A.1Determine whether a function is even, odd, or neither.P.F.IF.A.2Analyze qualities of exponential, polynomial, logarithmic, trigonometric, and rational functions and solve real-world problems that can be modeled with these functions (by hand and with appropriate technology).P.F.IF.A.3Identify the real zeros of a function and explain the relationship between the real zeros and the x-intercepts of the graph of a function (exponential, polynomial, logarithmic, trigonometric, and rational).P.F.IF.A.4Identify characteristics of graphs based on a set of conditions or on a general equation such as y = ax^2 + c.P.F.IF.A.5Visually locate critical points on the graphs of functions and determine if each critical point is a minimum, a maximum, or point of inflection. Describe intervals where the function is increasing or decreasing and where different types of concavity occur.P.F.IF.A.6Graph rational functions, identifying zeros, asymptotes (including slant), and holes (when suitable factorizations are available) and showing end-behavior.P.F.IF.A.7Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers (for example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n + 1) = f(n) + f(n - 1) for n ≥ 1).
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