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 Free 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 and use inverse functions Find and use inverse functions, including domain restrictions needed to make a function one-to-one. Compose functions and apply domain restrictions Compose functions in the correct order, simplify where appropriate, and apply restrictions imposed by the outer function. 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. Read values from a linear graph Read a coordinate directly off a straight-line graph on a grid, then state the y-value at a given x. Builds graph-interpretation skill where the value must be extracted from the diagram, not given in the text. Analyse rational functions and asymptotes Find asymptotes, intercepts, and behaviour of simple rational functions. Read the gradient of a linear graph Read the coordinates of two points off a straight-line graph, then calculate the gradient as rise over run. Builds the skill of extracting values from a diagram and combining them, not just reading a single value. Model with exponential functions Use exponential functions for growth and decay contexts. Read values from a curve Read a coordinate off a curved (parabola) graph on a grid, then state the y-value at a given x. Extends graph reading from straight lines to curves, where the height changes at different rates. Use logarithmic functions, domains and inverses Use logarithmic functions and interpret inverse relationships. Solve simultaneous equations from a graph Read the x-coordinate of the point where two straight lines cross - the solution of the pair of simultaneous equations.