CCSSAPhigh school
AP Precalculus — Gold Module
Functions, transformations, composition, and contextual interpretation — the core building blocks of AP Precalculus. Master how functions behave, how to transform them, and how to apply them to real-world situations.
4units
4topics
72questions
~2hours
Course Units
Learning objectives
- Determine domain and range from a graph or equation
- Apply the vertical line test to identify functions
- Evaluate functions using proper notation f(a)
- Evaluate piecewise-defined functions at boundary values
- Evaluate and simplify difference quotients as preparation for the concept of rate of change
Topics in this unit
Learning objectives
- Apply vertical shifts f(x)+k and horizontal shifts f(x-h)
- Distinguish inside transformations from outside transformations
- Apply vertical stretch af(x) and horizontal compression f(bx)
- Combine multiple transformations in correct order
- Distinguish -f(x) (reflection over x-axis) from f(-x) (reflection over y-axis)
Topics in this unit
Learning objectives
- Evaluate f(g(x)) by substitution
- Determine the domain of a composed function
- Distinguish f(g(x)) from g(f(x))
- Apply composition in real-world modeling contexts
Topics in this unit
Learning objectives
- Interpret function values in applied contexts (population, cost, decay)
- Translate between symbolic, graphical, verbal, and contextual representations
- Apply key concepts from Transfer and Contextual Interpretation in practice and assessment
- Explain how the same function can model different real-world phenomena depending on the context and units of the variables
Topics in this unit