2.2 Functions - AHL content

• Use composite functions in context: (f o g)(x)=f(g(x)).

• Find inverse functions, including necessary domain restrictions.

• Apply translations, reflections, vertical/horizontal stretches and composite transformations.

• Perform transformations on SL/AHL model functions and real-context functions.

• Understand order of transformations.

• 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.

• 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.