2. Functions

COURSE DESCRIPTION

This course delves into the concept of functions as a cornerstone of mathematical understanding within the IBDP Mathematics: Analysis and Approaches HL and SL curricula. Students will investigate the nature of functions through graphical, algebraic, and numerical representations. Beginning with linear and quadratic functions, the unit expands to include composite and inverse functions, exponential and logarithmic models, rational functions, and transformations. HL students further explore advanced function properties such as symmetry, rational behavior, and modulus graphs. The course emphasizes analysis, interpretation, and problem-solving using both algebraic techniques and technological tools.

LEARNING OUTCOMES

• Interpret and construct equations of straight lines, including parallel and perpendicular lines
• Use function notation; identify domain, range, and inverse functions through reflection
• Graph a wide variety of functions and analyze key features using technology
• Solve problems involving composite functions, identity functions, and inverses
• Explore quadratic functions and solve related equations and inequalities
• Determine the discriminant and interpret the nature of roots
• Graph reciprocal and simple rational functions, identifying vertical and horizontal asymptotes
• Understand and apply exponential and logarithmic functions in real-world contexts
• Solve equations analytically and graphically, using GDC tools effectively
• Perform and describe transformations of functions including translations, reflections, stretches, and compressions
• (HL) Apply factor and remainder theorems and derive relationships between roots of polynomials
• (HL) Analyze rational functions with complex numerators and denominators
• (HL) Identify and analyze odd, even, self-inverse functions, and impose domain restrictions where required
• (HL) Solve advanced inequalities algebraically and graphically, including modulus equations and inequalities

TOPICS COVERED

SL 2.1–2.11

• Linear equations
• Function notation, domain and range
• Graphs and key features
• Composite and inverse functions
• Quadratic and rational functions
• Exponential and logarithmic models
• Solving equations graphically and analytically
• Function transformations

AHL 2.12–2.16

• Polynomial theorems (factor, remainder)
• Rational function behavior and graphing
• Symmetric functions (odd, even, inverse)
• Inequalities including modulus functions