Functions
Functions for IB Applications and Interpretation SL: domain, range, linear, quadratic, inverse, exponential and circular models, with worked IB questions.
A function is a rule that assigns to each input value a single output value. It is the tool with which mathematics models the world: the cost of a taxi ride, the height of a ball, the growth of a population or the tide in a harbour. In this topic you learn to read and describe a graph (domain, range, intercepts, maxima and minima, asymptotes) and to work with the families that appear most often in the exam: linear, quadratic, the inverse function, exponential, integer powers with their asymptotes, and circular functions (sine and cosine). In the IB Applications and Interpretation SL course, the graphic display calculator (GDC) is the main tool: drawing, finding intercepts, maxima and minima, and solving equations. What is assessed is that you choose the model, use it well and interpret the result in context.
Recommended order
Follow the sections in order: functions and features of their graphs, linear functions and models, quadratic functions and models, the inverse function, exponential functions and models, integer power functions and asymptotes and circular functions. At the end you will find the IB exam questions, grouped by type.
Basic algebra and equations (topic 1) and basic trigonometry (topic 3).
Sections in this topic
Functions: domain, range and features of the graph
What a function is, how to find its domain and range, and how to read a graph: intercepts, increase, maxima, minima and symmetry. IB Applications SL.
3 worked examples Section 2Linear functions and linear models
Gradient, equation of a line, parallel and perpendicular lines, piecewise functions and linear models with equilibrium. IB Applications SL.
3 worked examples Section 3Quadratic functions and quadratic models
Parabolas, vertex, axis of symmetry, intercepts and discriminant; general, factored and vertex forms, and models with maxima and minima. IB SL.
3 worked examples Section 4Inverse function: how to find it and what it means
What an inverse function is, when it exists, how to calculate it, how domain and range change, its graph reflected in y = x, and composition. IB SL.
3 worked examples Section 5Exponential functions and models of growth and decay
How to work with exponential functions f(x)=k·a^x+c, their horizontal asymptote, and population and cooling models. IB Applications and Interpretation SL.
3 worked examples Section 6Integer power functions and vertical and horizontal asymptotes
Graphs with integer powers of x, vertical and horizontal asymptotes, and how to solve with the GDC. IB Applications and Interpretation SL.
3 worked examples Section 7Circular functions: sine, cosine, amplitude, period and periodic models
Graphs of sine and cosine, amplitude, period and midline of f(x)=a·sin(bx)+c, and models of tides, Ferris wheels and temperatures. IB SL.
3 worked examples End of topicIB exam questions for topic 6
IB exam questions on functions: domain, linear, quadratic, inverse, exponential, power and circular functions, by type and level, with step-by-step solutions.
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