Build a rigorous understanding of functions through multiple representations, linear and quadratic models, and transformations. Connect symbolic forms to tables, graphs, and real-world meanings.
Understand inputs/outputs, domain/range, and three representations: formula, table, graph.
Analyze y = mx + b: slope as rate of change, intercepts, average rate equals slope.
Study y = ax² + bx + c and vertex form a(x - h)² + k: symmetry, vertex, zeros, max/min.
Master vertical/horizontal shifts and scaling: f(x)+k, f(x+h), k·f(x), f(kx).
Linear cost/revenue models, break-even analysis, optimization
Quadratic motion models, vertex as max/min height
Signal processing and scaling transformations