Working with functions
Apply algebraic techniques and work with linear, quadratic, cubic, reciprocal, absolute value and piecewise functions.
Algebra and Functions · MAV-11-01
Sub-topics
Algebraic techniques
Apply index laws to simplify expressions with integer indices, expand binomial products, factorise quadratics, rationalise surds, and use the discriminant to determine the nature and number of roots of a quadratic.
Introduction to functions
Determine whether a graph represents a function using the vertical line test, state the domain and range, evaluate function rules, find zeroes, and classify functions as even, odd or neither.
Linear and quadratic functions
Write equations of lines in gradient-intercept form, identify parallel and perpendicular lines, convert quadratic equations to vertex form by completing the square, and solve simultaneous systems of one linear and one quadratic equation.
Cubic and reciprocal functions
Identify x-intercepts and end behaviour of cubic functions in factored form, sketch and analyse reciprocal functions of the form , and match equations to graphs by justifying key features.
Properties of functions
Evaluate composite functions, analyse piecewise-defined functions for continuity and points of discontinuity, and solve and sketch absolute value functions.
Variation and modelling
Identify direct and inverse variation from equations and tables, determine the constant of variation from data, and construct and evaluate variation models from two data points.