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HL AA – Functions

Learning outcomes
 Understanding the concept of a function. Substitute and solve equations using algebra. Understand the terms domain and range. Find the inverse of a function Understand the terms one-to-one; many-to-one; one-to-many and their applications to functions and inverses. Graph functions with and without a GDC. Note key points on graphs (intersection with axes, maximum and minimum). Understand and use composite functions. Substitute and solve equations using graphs, including composite functions. Using reciprocal graphs, including finding asymptotes from functions with and without sketches. Solve intersection of functions using a GDC. Transformation of functions: reflections in x and y axes; reflection in y=x line; translations; vertical and horizontal stretches. Using the inverse function and the reflection to solve equations. Odd and even functions Sum and roots of a quadratic equation (alpha and beta values). Sum and roots of all polynomial functions, where order is greater than 2. Inequalities of functions and their graphs. The reciprocal of a function and its graph. The modulus of a function and its graph. Factor theorem of polynomials. Remainder theorem of polynomials.