Reasoning with Equations and Inequalities
Represent and solve equations and inequalities graphically.
Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
Build a function that models a relationship between two quantities.
Write a function that describes a relationship between two quantities.
Determine an explicit expression, a recursive process, or steps for calculation from a context.
Understand congruence in terms of rigid motions.
Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
Similarity, Right Triangles, and Trigonometry
Understand similarity in terms of similarity transformations.
Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
The Complex Number System
(+) Use complex numbers in polynomial identities and equations.
Extend polynomial identities to the complex numbers.