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The student will investigate and analyze function (linear, quadratic, exponential, and logarithmic) families and their characteristics. Key concepts include: a) continuity; b) local and absolute maxima and minima; c) domain and range; d) zeros; e) intercepts; f) intervals in which the function is increasing/decreasing; g) end behaviors; and h) asymptotes.
The student will use knowledge of transformations to write an equation, given the graph of a function (linear, quadratic, exponential, and logarithmic).
The student will collect data and generate an equation for the curve (linear, quadratic, exponential, and logarithmic) of best fit to model real-world problems or applications. Students will use the best fit equation to interpolate function values, make decisions, and justify conclusions with algebraic and/or graphical models.
The student will transfer between and analyze multiple representations of functions, including algebraic formulas, graphs, tables, and words. Students will select and use appropriate representations for analysis, interpretation, and prediction.
The student will determine optimal values in problem situations by identifying constraints and using linear programming techniques.