A2.F.2

The student will investigate and analyze characteristics of square root, cube root, rational, polynomial, exponential, logarithmic, and piecewise-defined functions algebraically and graphically.

A2.F.2.aDetermine and identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically, including graphs with discontinuities.A2.F.2.bCompare and contrast the characteristics of square root, cube root, rational, polynomial, exponential, logarithmic, and piecewise-defined functions.A2.F.2.cDetermine the intervals on which the graph of a function is increasing, decreasing, or constant.A2.F.2.dDetermine the location and value of absolute (global) maxima and absolute (global) minima of a function.A2.F.2.eDetermine the location and value of relative (local) maxima or relative (local) minima of a function.A2.F.2.fFor any value, 𝑥, in the domain of 𝑓, determine 𝑓(𝑥) using a graph or equation. Explain the meaning of 𝑥 and 𝑓(𝑥) in context, where applicable.A2.F.2.gDescribe the end behavior of a function.A2.F.2.hDetermine the equations of any vertical and horizontal asymptotes of a function using a graph or equation (rational, exponential, and logarithmic).A2.F.2.iDetermine the inverse of a function algebraically and graphically, given the equation of a linear or quadratic function (linear, quadratic, and square root). Justify and explain why two functions are inverses of each other.A2.F.2.jGraph the inverse of a function as a reflection over the line 𝑦 = 𝑥.A2.F.2.kDetermine the composition of two functions algebraically and graphically.
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