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...
Advanced Topics

Function Models and Families

Recognizing Different Types of Functions

Functions come in many "families," each with unique features and uses. Common function families include:

  • Linear Functions: Straight lines, constant rate of change.
  • Quadratic Functions: Parabolas, involve \( x^2 \).
  • Exponential Functions: Rapid growth or decay, involve \( a^x \).
  • Absolute Value Functions: V-shaped graphs, measure distance from zero.

Why Families Matter

By recognizing which family a function belongs to, you can predict its behavior and choose the right tools to analyze or solve problems.

Function Models

Real-world phenomena like population growth, projectile motion, and temperature changes can all be modeled by different function types.

Examples

  • Population growth can often be modeled with exponential functions.

  • A ball's path after being thrown can be modeled by a quadratic function.

In a Nutshell

Different families of functions model different patterns and behaviors.

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Functions in Finance