OGM.13.FN
Open Global Math Standards 2026™ · 12th Grade
Advanced Functions, Equations, Inequalities, and Transformations
Grade12th Grade
SubjectMath
Levelstrand
Child standards (6)
- OGM.13.FN.1Analyze quadratic functions and equations, completing the square, evaluating the discriminant for real, repeated, or complex roots, and solving linear and quadratic inequalities in one and two variables graphically and using interval and set notation.
- OGM.13.FN.2Solve simultaneous linear and non-linear systems algebraically by substitution and elimination, and interpret solutions as intersection points of curves.
- OGM.13.FN.3Define formal functions, mappings, domains, and ranges; determine composite functions $f(g(x))$, evaluate non-commutativity of composition, decompose composite functions, and find inverse functions $f^{-1}(x)$ with domain restrictions across algebraic, graphical, and numeric representations.
- OGM.13.FN.4Analyze, graph, and model polynomial, rational, power, modulus, and piecewise/step functions; identify key features including symmetry (even/odd), zeros, local extrema, intervals of increase/decrease, end behavior using infinity notation, and horizontal, vertical, and oblique asymptotes.
- OGM.13.FN.5Apply single and combined transformations $y = af(bx - c) + d$ to parent graphs, analyzing the geometrical effects of vertical/horizontal stretches, compressions, reflections, and translations.
- OGM.13.FN.6Investigate continuity and types of discontinuities (removable, jump, infinite) of functions over $(-\infty, \infty)$, describing one-sided limits and behavior around discontinuities while evaluating technological limitations of graphing tools.