FunctionsBy: Samantha Adams

Technology in Education

Key Concepts

• What is a function?

• What is function notation?

• How to recognize functions by graphs

• Let’s start with a example

Example #1

At the beginning of the year each student is assigned a teacher.

Johnny Mrs. Morgan

Sally Mrs. Brown

Jane Mr. Black

Michael Mr. White

Doug Mrs. Jones

So for each student there is one teacher.

This represents a function.

What is a function…

• A relationship between two or more sets of data so that:– The x-variable (domain) corresponds to only ONE y-variable (range)

• Let’s look at an example with numbers

Example #2

Tell whether or not these are functions..

a. { (0,1), (3,6), (4,3), (1,8) }

b. { (9,3), (4,8), (1,9), (3,5) }

c. { (9,4), (9,6), (9,1), (9,2) }

Example #2 Explanation

• First list the domain and range for each– A. domain {0,3,4,1} range {1,6,3,8}

B. domain {9,4,1,3} range {3,8,9,5}C. domain {9,9,9,9} range {4,6,1,2}

• Notice that in A. and B. each x corresponds to one y– Therefore it is a function

• In C. one x corresponds to four (4) y– Therefore it is not a function

What is function notation?

• An equation y= 2x+5

• To be function notation change the y to f(x)

• Therefore f(x)= 2x+5– In f(x) the x is what is plugged in for x in the

equation

– Let’s take a look at an example

Example #3

• Solve f(x)= 5x+9 X= -2 X= -1 X= 0 X= 1 X= 2

• Remember plug the numbers in for x

Take X= -2, 2

• Solve f(x)= 5x+9

X= -2 F(-2)= 5(-2)+9

F(-2)= -10+9

F(-2)= -1

• Solve f(x)= 5x+9

X= 2 F(2)= 5(2)+9

F(2)= 10+9

F(2)= 19

Graphs of Functions

In order to tell if the graph is a function it must pass the vertical line test (VLT).

- VLT is done by drawing a vertical line through any point of the graph and it

only cuts the line once.

Graph 1 Graph 2 Graph 3

Graph of Functions Cont'd

• The first and third graphs are both examples of functions– The dashed line cuts the graph once

• The middle graph is not a function– The dashed line passes through three (3) times

Graph 3Graph 2Graph 1

Overview

• A function is a relation between x (domain) and y (range).– Where each x corresponds to one y

• How to put an equation in function notation– Change y to f(x)

• Lastly how to recognize if a graph is that of a function– It has to pass the vertical line test

END