Functions

Learn and practice identifying and graphing different types of functions with interactive resources from GeoGebra.

Middle School

GRADES 6-8

Graphing Linear Functions Using Ordered Pairs

Use ordered pairs derived from tables, algebraic rules, or verbal descriptions to graph linear functions.

탐구

GR. 6-8

Tables, Graphs, and Linear Equations

Intercepts of Linear Relations

Identify and interpret the intercepts of a linear relation in number and word problems.

실습

GR. 6-8

Word Problems Involving Intercepts

Point Point Form of a Line

Write the equation of and graph linear relationships given two points on the line.

탐구

GR. 6-8

Filling Points with Lines

실습

GR. 6-8

Writing the Equation of a Line Using Two Points

실습

GR. 6-8

Collecting Points Using Lines Game

Point Slope Form of Line

Write the equation of and graph linear relationships given the slope and one point on the line.

탐구

GR. 6-8

Transforming Lines by Shifting

Properties of Linear Functions, Graphs, and Equations

Interpret and compare properties of linear functions, graphs, and equations.

실습

GR. 6-8

Creating a Line with the Given Slope

Relations and Functions

Define and distinguish between relations and functions, dependent and independent variables, and domain and range; identify whether relations are functions numerically and graphically.

탐구

GR. 6-8

Identifying Domain and Range

탐구

GR. 6-8

Dependent and Independent Variables

탐구

GR. 6-8

Identifying Functions Using Diagram Mapping

탐구

GR. 6-8

The Vertical Line Test

실습

GR. 6-8

Writing Domain and Range from a Set of Points

Slope as Rate of Change

Describe the slope of a line given in the context of a problem situation; compare rates of change in linear relationships represented in different ways.

실습

GR. 6-8

Making Slope Triangles

실습

GR. 6-8

Comparing Rates of Change in a Car Race

Slope Intercept Form of a Line

Write the equation of and graph linear relationships given the slope and y-intercept.

탐구

GR. 6-8

Relating the Slope and Intercept of a Line to Its Graph

실습

GR. 6-8

Writing the Equation of a Line

실습

GR. 6-8

Graphing the Line

Slope of a Line

Find the slope of a line given two points on a line, a table of values, the graph of the line, or an equation of the line in number and word problems.

실습

GR. 6-8

Calculating the Slope of a Line

High School

GRADES 9-12

Composition and Inverse of Functions

Find the inverse of a function or relation. Verify that two functions are inverses using their graphs or composition of functions.

탐구

GR. 9-12

Introducing Inverses of Functions

탐구

GR. 9-12

Inverses of Linear Functions

Domain and Range of Special Functions

Write and graph special functions (step, constant, and piecewise) and identify the domain and range.

탐구

GR. 9-12

Domain and Range of Constant Functions

탐구

GR. 9-12

Domain and Range of Piecewise Functions

실습

GR. 9-12

Writing Domain and Range of a Piecewise Function

탐구

GR. 9-12

Connecting Piecewise Functions to Graphs and Contexts

실습

GR. 9-12

Writing Piecewise Functions from Graphs

탐구

GR. 9-12

Modeling Real-World Costs with Step Functions

Functions and Function Notation

Use and interpret function notation in number and word problems; determine a value of the function given an element of the domain.

탐구

GR. 9-12

Exploring Linear Function Notation

실습

GR. 9-12

Evaluating Linear Functions

탐구

GR. 9-12

Exploring Exponential Function Notation

실습

GR. 9-12

Evaluating Exponential Functions

Increasing and Decreasing Functions

Describe the intervals for which a function is increasing or decreasing.

탐구

GR. 9-12

Changing Behavior of Linear Intervals

탐구

GR. 9-12

Changing Behavior of Exponential Functions

탐구

GR. 9-12

Changing Behavior of Quadratic Functions

실습

GR. 9-12

Increasing or Decreasing Intervals of a Quadratic Function

탐구

GR. 9-12

Changing Behavior of Open Graphs

Real-World Phenomena as Functions

Describe graphically, algebraically and verbally real-world phenomena as functions; identify the independent and dependent variables and any constraints of the domain or range.