Learning Domain: Secondary Mathematics III

Standard: Functions — Building Functions

Indicator: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Note the effect of multiple transformations on a single function and the common effect of each transformation across function types. Include functions defined only by a graph. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

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Learning Domain: Secondary Mathematics III

Standard: Algebra — Arithmetic With Polynomials and Rational Expressions

Indicator: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

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Learning Domain: Secondary Mathematics III

Standard: Algebra — Arithmetic With Polynomials and Rational Expressions

Indicator: Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).

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Learning Domain: Secondary Mathematics III

Standard: Functions — Interpreting Functions

Indicator: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Compare and contrast square root, cubed root, and step functions with all other functions.

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Learning Domain: Secondary Mathematics III

Standard: Functions — Interpreting Functions

Indicator: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

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Learning Domain: Secondary Mathematics III

Standard: Algebra — Arithmetic With Polynomials and Rational Expressions

Indicator: Prove polynomial identities and use them to describe numerical relationships.

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