Functions & Graphs

This module develops a mature view of the function concept, moving beyond formulae to the mapping idea and its graphical signature. Learners work with domain, range, composition, inverse and transformations, and they study the main families of functions used throughout the STRAIT programme. Visual, numerical and symbolic representations are related explicitly. By its end, learners can read a graph, write a function and move between the two with confidence.

Learning Outcomes

Determine the domain and range of standard real-valued functions (apply)

Compose and invert functions and justify when an inverse exists (apply)

Sketch and interpret graphs of polynomial, rational, exponential, logarithmic and piecewise functions (apply)

Describe the effect of translations, reflections, stretches and reflections on a graph (analyse)

Classify functions as even, odd, periodic, injective or surjective where appropriate (analyse)

Evaluate continuity and asymptotic behaviour informally (evaluate)

Construct a function to model a described situation and critique the model (create)

Compare symbolic, graphical and tabular representations of the same function (analyse)

Topics Covered

Definition of a function and the vertical-line test

Domain, range, codomain

Function notation and evaluation

Composition of functions

Inverse functions and the horizontal-line test

Linear and quadratic functions

Polynomial and rational functions

Exponential and logarithmic functions

Absolute-value and piecewise-defined functions

Transformations of graphs

Even/odd symmetry and periodicity

Asymptotes, holes and end behaviour

Continuity: an informal view

Function modelling in context

Graph reading and interpretation

Skills Developed

Reading and sketching graphs Translating word problems into functional form Applying transformations systematically Composition and inversion Identifying domain restrictions Interpreting asymptotes Classifying symmetry Checking a model against data

Suggested Resources

STRAIT Functions & Graphs workbook (TutorDA, 2025)

Stewart, J. Precalculus: Mathematics for Calculus (7th ed.), chapters 2-4

Khan Academy: Functions playlist

3Blue1Brown: Essence of calculus (early episodes on functions)

Desmos graphing calculator (desmos.com/calculator)

GeoGebra function explorer

TutorDA practice bank: A-M2 drill sets

Assessment

Assessment pairs a written exam that stresses graphical interpretation and symbolic agility with a modelling task in which learners build and defend a function for a real situation.

Written examination (2 hr)55%

Modelling task and coursework45%

Practice bank: 197 MCQs · Timed mock & self-paced modes

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