Geometric Transformations of General Functions

7 lessons

Goal

Apply single and multi-step vertical and horizontal translations, stretches, compressions, and reflections to arbitrary functions y = f(x).

Vertical and Horizontal Translations: f(x) + a and f(x + a)

7 lessons

0 of 7 done

Standards Covered

Curriculum Framework

6 lessons

Master the formal mapping definition of functions, algebraic and contextual domain-range analysis, and advanced function notation.

8 lessons

Analyze, interpret, and sketch critical graph features across diverse function families including extrema, behavior, and symmetry.

6 lessons

Analyze, evaluate, and sketch piecewise-defined, greatest integer (floor/ceiling), and absolute value (modulus) functions.

6 lessons

Perform algebraic arithmetic on functions, construct composite functions, and evaluate nested domains.

7 lessons

Determine invertibility, construct inverses algebraically and graphically, restrict domains, and verify inverse relationships via composition.

7 lessons

Apply single and multi-step vertical and horizontal translations, stretches, compressions, and reflections to arbitrary functions y = f(x).

6 lessons

Analyze arithmetic progressions explicitly and recursively, compute nth terms, and evaluate arithmetic series in sigma notation.

8 lessons

Analyze geometric progressions, evaluate partial sums using sigma notation, and determine convergence and infinite sums for |r| < 1.