Common Core: High School - Functions

This subject covers the essential concepts and applications of functions in high school mathematics, preparing students for advanced mathematical reasoning.

Understanding FunctionsFunction Notation and EvaluationGraphing Functions
Transformations of FunctionsInverse and Composite FunctionsFunction Models and Families
Functions in FinanceFunctions in Science and EngineeringFunctions in Everyday Life
Identifying Function Types on TestsChecking Your Work with the Vertical Line Test
Understanding Functi...Function Notation an...Graphing FunctionsTransformations of F...Inverse and Composit...Function Models and ...Functions in FinanceFunctions in Science...Functions in Everyda...Identifying Function...Checking Your Work w...
Practical Applications

Functions in Science and Engineering

Modeling the World with Functions

Scientists and engineers use functions to describe and predict everything from the speed of a car to the brightness of a star.

Physics Examples

  • The height of a dropped ball: \( h(t) = h_0 - 16t^2 \) (a quadratic function).
  • The cooling of hot coffee: \( T(t) = T_{\text{room}} + (T_0 - T_{\text{room}})e^{-kt} \) (an exponential function).

Engineering Applications

Functions help design bridges, buildings, and roller coasters by modeling forces and motion.

Examples

  • Predicting how long it takes for ice to melt using temperature functions.

  • Calculating the trajectory of a rocket with a quadratic function.

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Functions in Everyday Life