A.F.2: The student will investigate, analyze, and compare characteristics of functions, including quadratic, and exponential functions, and model quadratic and exponential relationships.

The student will investigate, analyze, and compare characteristics of functions, including quadratic, and exponential functions, and model quadratic and exponential relationships.

A.F.2.aDetermine whether a relation, represented by a set of ordered pairs, a table, a mapping, or a graph is a function; for relations that are functions, determine the domain and range.A.F.2.bGiven an equation or graph, determine key characteristics of a quadratic function including π‘₯-intercepts (zeros), 𝑦-intercept, vertex (maximum or minimum), and domain and range (including when restricted by context); interpret key characteristics as related to contextual situations, where applicable.A.F.2.cGraph a quadratic function, 𝑓(π‘₯), in two variables using a variety of strategies, including transformations 𝑓(π‘₯) + π‘˜ and π‘˜π‘“(π‘₯), where π‘˜ is limited to rational values.A.F.2.dMake connections between the algebraic (standard and factored forms) and graphical representation of a quadratic function.A.F.2.eGiven an equation or graph of an exponential function in the form 𝑦 = π‘Žπ‘Λ£ (where 𝑏 is limited to a natural number), interpret key characteristics, including 𝑦-intercepts and domain and range; interpret key characteristics as related to contextual situations, where applicable.A.F.2.fGraph an exponential function, 𝑓(π‘₯), in two variables using a variety of strategies, including transformations 𝑓(π‘₯) + π‘˜ and π‘˜π‘“(π‘₯), where π‘˜ is limited to rational values.A.F.2.gFor any value, π‘₯, in the domain of 𝑓, determine 𝑓(π‘₯) of a quadratic or exponential function. Determine π‘₯ given any value 𝑓(π‘₯) in the range of 𝑓 of a quadratic function. Explain the meaning of π‘₯ and 𝑓(π‘₯) in context.A.F.2.hCompare and contrast the key characteristics of linear functions (𝑓(π‘₯) = π‘₯), quadratic functions (𝑓(π‘₯) = π‘₯Β²), and exponential functions (𝑓(π‘₯) = 𝑏ˣ) using tables and graphs.
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