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2 Functions

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  1. 2.1 Functions - SL content

    1. SL 2.1Straight lines

      • Use gradient, intercepts and forms of a straight line. • Know parallel gradients m1=m2 and perpendicular gradients m1m2=-1.

    2. SL 2.2Functions and inverses

      • Understand function, domain, range, graph and function notation. • Interpret functions as mathematical models. • Inverses undo functions, reflect in y=x and exist for one-to-one functions.

    3. SL 2.3Graphing functions

      • Draw/sketch graphs from equations, contexts or technology. • Label axes and key features, including sums and differences of functions.

    4. SL 2.4Key graph features

      • Determine maxima, minima, intercepts, symmetry, vertex, roots/zeros and asymptotes. • Use technology to find intersections of curves or lines.

    5. SL 2.5Modelling with functions

      • Use linear, piecewise linear, quadratic, exponential, direct/inverse variation, cubic and sinusoidal models. • Interpret key parameters such as roots, vertex, asymptotes, amplitude, period and principal axis. • Use technology where appropriate to find roots and fit or interpret models.

    6. SL 2.6Modelling process

      • Choose an appropriate model and reasonable domain for a context. • Find model parameters using technology, initial conditions or substitution of points. • Test, reflect on, interpret and use models; recognize dangers of extrapolation.

  2. 2.2 Functions - AHL content

    1. • Use composite functions in context: (f o g)(x)=f(g(x)). • Find inverse functions, including necessary domain restrictions.

    2. • Apply translations, reflections, vertical/horizontal stretches and composite transformations. • Perform transformations on SL/AHL model functions and real-context functions. • Understand order of transformations.

    3. • 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.

    4. • 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.