What you’ll learn4 learning objectivesChoose one objective for a focused lesson, or study the complete topic.—AHL 2.7 (HL)—Composite and inverse functions• Use composite functions in context: (f o g)(x)=f(g(x)).• Find inverse functions, including necessary domain restrictions.Syllabus objective—AHL 2.8 (HL)—Graph transformations• Apply translations, reflections, vertical/horizontal stretches and composite transformations.• Perform transformations on SL/AHL model functions and real-context functions.• Understand order of transformations.Syllabus objective—AHL 2.9 (HL)—Further modelling functions• Model with half-life exponential, natural logarithmic, sinusoidal, logistic and piecewise functions.• For sinusoidal models, use radians unless degrees are specified; phase shift is horizontal translation.• Logistic models use carrying capacity L; piecewise models may require continuity of parameters.Syllabus objective—AHL 2.10 (HL)—Logarithmic scaling and linearization• Scale very large/small numbers using logarithms.• Linearize data with logarithms to test exponential or power relationships.• Interpret log-log and semi-log graphs; drawing/sketching them is not required in exams.Syllabus objective