Unit 1

Foundations of Functions

Review and extend function concepts: domain, range, composition, inverses, transformations, and piecewise functions.

Unit 1 · 9 pages

Lessons

Unit overview, essential questions, learning objectives, and vocabulary list for Unit 1 Functions.

Define functions, use function notation, evaluate functions, and determine if a relation is a function.

Find domain and range from graphs, tables, and equations. Use interval and set-builder notation.

Calculate average rate of change, identify increasing/decreasing intervals, and locate local extrema.

Form composite functions (f∘g)(x), evaluate compositions, and find the domain of a composite.

Apply vertical/horizontal shifts, reflections, and stretches/compressions to parent functions.

Graph absolute value functions, identify vertex and axis of symmetry, and solve absolute value equations graphically.

Verify inverse functions, find f⁻¹(x) algebraically, and restrict domains to make functions invertible.

Consolidate your understanding of functions, domain and range, composition, transformations, and inverses.