Functions and equations

Outline of IB Mathematics Higher Level

Concept of function (domain, range, image),Odd and even functions,Composite functions, Identity function,One-to-one and many-to-one functions
Inverse function, The graph of a function, Investigation of key features of graphs, such as maximum and minimum values, intercepts, horizontal and vertical asymptotes and symmetry,and consideration of domain and range.
Transformations of graphs: translations, stretches, reflections in the axes. The graph of the inverse function as a reflection in y = x. Rational function, exponential function and logarithmic function.
Polynomial functions and their graphs. The factor and remainder theorems. The fundamental theorem of algebra.
Solving quadratic equations using the quadratic formula. Use of the discriminant to determine the nature of the roots.
Solving polynomial equations both graphically and algebraically. Sum and product of the roots of polynomial equations.
Use of technology to solve a variety of equations, including those where there is no appropriate analytic approach.
Graphical or algebraic methods, for simple polynomials up to degree 3. Use of technology for these and other functions.

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