Functions, Domain, Range, and Piecewise Representations

Evaluate functions, determine domain and range across multiple notations, and construct and analyze piecewise-defined functions.

Analyze, graph, convert, and model with linear functions in all forms, including slope relationships and direct variation.

Analyze, convert, graph, and model quadratic functions across standard, vertex, and factored forms.

Model growth and decay, graph exponential and logarithmic functions across bases 2, 10, and e, and solve equations.

Graph and analyze parent functions (absolute value, square root, cube root, reciprocal, cubic, sine/cosine) and model inverse variation.

Apply, identify, and formulate vertical and horizontal translations, stretches, compressions, and reflections across all function families.

Determine inverse functions algebraically, verify inverses via composition and graphical symmetry, and restrict domains for one-to-one invertibility.

Represent arithmetic and geometric sequences recursively and explicitly, link to linear/exponential growth, and derive and evaluate geometric series.

Explain graphs as solution sets, find intersection coordinates of y = f(x) and y = g(x) to solve f(x) = g(x), and compare growth models.