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For absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic functions, the student will a) recognize the general shape of function families; and b) use knowledge of transformations to convert between equations and the corresponding graphs of functions.
The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve practical problems, including writing the first 𝑛 terms, determining the 𝑛ᵗʰ term, and evaluating summation formulas. Notation will include Σ and 𝑎ₙ.
The student will investigate and analyze linear, quadratic, absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic function families algebraically and graphically. Key concepts include a) domain, range, and continuity; b) intervals in which a function is increasing or decreasing; c) extrema; d) zeros; e) intercepts; f) values of a function for elements in its domain; g) connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs; h) end behavior; i) vertical and horizontal asymptotes; j) inverse of a function; and k) composition of functions, algebraically and graphically.
The student will investigate and describe the relationships among solutions of an equation, zeros of a function, 𝑥-intercepts of a graph, and factors of a polynomial expression.