Competences

• • a)Represent functions namely algebraically, graphically, verbally and numerically;
  • b)Present functions graphically and explain key features of function graphs, also by using graphing calculators and software, such as Geogebra and Desmos, and online platforms to teach and explore functions interactively;
  • c)Ensure collaborative experiences to explore and solve problems related to functions and graphs;
  • d)Deal with functions in various contexts and foster critical thinking skills;
  • e)Interpret, represent, and communicate functional relationships using multiple representations and apply these skills to real-world contexts and pedagogical practices;
  • f)Identify, discuss and address common students` misconceptions and errors related to functions and graphs;
  • g)Perform operations on functions, such as addition, subtraction, multiplication, division and composite functions;
  • h)Plot graphs accurately, and draw proper sketches from properties and learnt behaviours of graphs;
  • i)Interpret and analyse graphs extracting important information namely the maximum and minimum points, intercepts, increasing and decreasing behaviour and points of inflection;
  • j)Apply and recognise transformations such as translation, reflection, stretches and compressions on the graph of a function.

Knowledge

• a)Identify  and discuss the different types of functions, domain range and mappings;
• b)Recognise and define functions and their properties from equations, diagrams and from the given values, also about continuity, increasing/decreasing behaviours, even and odd functions;
• c)Interpret different models of real-life situations, such as population growth, financial models, physics problems, scatter graphs and line of best fit graphs, related properties and solutions;
• d)Identify strategies to solve various types of equations and inequalities using graphical methods;
• e)Explain the concepts of the inverse functions, the reciprocal, the square root and the modulus of a function and how to determine it graphically and algebraically from a given equation;
• f)Gain knowledge on how to work with piecewise defined functions and periodic functions, including graphing and analysing them;
• g)Explain and interpret parametric and polar coordinates and their equations, their analysis and graphing interpretations;
• h)Deal with the theoretic knowledge of functions and graphs  such as domain, codomain, range, plotting functions and the ability to explain them clearly through examples;
• i)Deal with the different types of functions, their properties and applications namely linear, quadratic, cubic, quartic, exponential, logarithmic, rational, and curve fitting situations, also transformations, inverse, reciprocal, square root, and parametric and polar graphs.
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Skills

• • a)Show and explain clearly the concepts related to functions and graphs using appropriate teaching methods and tools;
  • b)Analyse and interpret graphs; explain how changes in equations change the graph including shifts, stretches and reflections;
  • c)Solve equations involving functions, finding roots and evaluate the significance of these solutions in various contexts;
  • d)Perform and describe transformations such as translations, scaling, and rotations on functions and their corresponding graphs;
  • e)Show proficiency in using graph calculators, and/or educational software, and other digital tools to explain and teach functions and their graphs;
  • f)Develop precise mathematical language to describe and explain functions and their graphs;
  • g)Create and use visual aids effectively to support teaching and the knowledge;
  • h)Show how to interpret and analyse graphical data such as trends, making predictions and explaining the relationship between variables;
  • i)Discuss, draw and manipulate the concepts discussed;
  • j)Use online resources and platforms confidently so that mathematics can be visualised better.