Mathematics: Analysis and Approaches SL

Functions

Core function skills for IB Mathematics: Analysis and Approaches SL, including features of quadratics, transformations, inverse functions, and modelling language.

Identify key features of quadratic functions Find intercepts, axis of symmetry, vertex, domain, and range from a quadratic in expanded or factorised form, with solution language suitable for IB markschemes. Interpret transformations in vertex form Read vertex form of a quadratic to identify translations, reflection, vertical stretch, vertex, axis of symmetry, y-intercept, and range. Complete the square for quadratic functions Convert an expanded quadratic into vertex form, then identify the vertex, axis of symmetry, and range using IB-style reasoning. Find inverse linear functions Find and interpret the inverse of a linear function using rearrangement, function notation, and substitution checks. Compose linear functions Find and evaluate composite linear functions using function notation, substitution order, and simplified algebra. Evaluate functions and use notation Evaluate functions, interpret notation, and distinguish inputs from outputs. Find domain and range Determine domain and range from algebraic rules and graphical information. Analyse rational functions and asymptotes Find asymptotes, intercepts, and behaviour of simple rational functions. Model with exponential functions Use exponential functions for growth and decay contexts. Model with logarithmic functions Use logarithmic functions and interpret inverse relationships.