FUNCTIONS The Big Idea. Functions are the tool used for mathematically modeling all types of real-world change. The use of Functions allow people to analyze.

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Presentation transcript:

FUNCTIONS The Big Idea

Functions are the tool used for mathematically modeling all types of real-world change. The use of Functions allow people to analyze and understandchange.

A change in one variable can cause or have a corresponding effect on another. What are some change relationships that would interest you?

Functions are relationships or rules that uniquely associate members of one set with members of another set. The way change in one variable affects change in another.

It is a study of joint variation of variables. A rule that explains how the first (independent) variable affects the second (dependent) variable.

Functions help you find regularity in all mathematics. You can SEE, GENERALIZE, and REPRESENT relationships in which there are variables to be related.

Five Ways to Represent a Function. I.Contextual Representations What are you interested in finding out?

II. Table Representation (T-chart ) Put hypothetical values in the table. List the values for the independent variable (include ‘0’) ***Make sure you develop an equation.***

The dependent variable is a function of the independent variable

A is worth a thousand words! IV. Graphical Representations Graphs provide a visual of the relationship between your variables. * Sometimes the graph may not make sense for all portions of the graph.

V. Equations General form of a linear equation y=mx+b ***Equations make it easier to understand what is happening in a relationship.***

y = mx+b m tells us how quickly or steeply the line goes up or down moving from left to right. b tells us where the graph will cross the y-axis. Equations make it easier to calculate values of the function.

All 5: Contextual Representation Table Representation Language Expression Graphical Representation, and an Equation represent the same relationship.