1. 4.6 Formalizing relations and functions
To determine whether a relation is a function AND to find the domain and range using function notation.
Day 1

2. Relation: pairing of numbers in one set (the domain) with numbers in another set (the range). (often put in an ordered pair)
Domain:
The input values (x-values)
Range:
The output values (y-values)
Example: a motion detector stores input values (times) and output values (heights) as an egg is tracked as it is dropped from 10 ft. above the ground.
{(0,10), (.1, 9.8), (.2, 9.4), (.3, 8.6)}
{(0,10), (.1, 9.8), (.2, 9.4), (.3, 8.6)}
Domain:
{0, .1, .2, .3}
Range:
{8.6, 9.4, 9.8, 10}

3. Function: a relation where one value in the domain is paired with exactly one value of the range.
Find the domain and range and determine if the relation is a function.
Example 1
Input x
Output y 2 4 6 8 9 11 10 13
Example 2
Input x
Output y 2 9 6 10 11
Example 3
Input x
Output y 2 3 4 7 5 9 6
Domain: {2, 6, 9, 10}
Range: {4, 8, 11, 13}
Yes, it’s a function
Domain: {2, 6, 10, 11}
Range: {9}
Yes, it’s a function
Domain: {2, 7, 9}
Range: {3, 4, 5, 6}
NO, it’s not a function

4. Are the following graphs functions? –use the vertical line test
Not a function

5. Pg 271: 1,2,7-15, 48-50 function Not a function
Are the following graphs functions? Use the vertical line test
function
Not a function
Pg 271: 1,2,7-15, 48-50

6. YES {(0,10), (.1, 9.8), (.2, 9.4), (.3, 8.6)} function:? Domain:
{(0,10), (.1, 9.8), (.2, 9.4), (.3, 8.6)}
Use a mapping diagram to determine whether the relation is a function.
Domain:
{0, .1, .2, .3}
Range:
{10, 9.8, 9.4, 8.6}
Pg 271: 1,2,7-15, 48-50
Domain:
Range: .1 .2 .3 10
function:?
YES

7. Function Notation Name a fast car New School: Function Notation
f(x) = 2x + 3
f(4) = 2(4) + 3
f(4) = 8 + 3
f(4) = 11
(4, 11)
Name a slow car
Old School:
Equation
y = 2x + 3
Solve y = 2x + 3 when x = 4
y = 2(4) + 3
y = 8 + 3
y = 11
(4, 11)

8. Function notation: uses parenthesis to name the input or independent variable for the function.
f(x) is pronounced f of x
It does not mean to multiply f and x together.
y = f(x)
Equation
y = 4x + 8
y = -7x + 5
y = 5x – 7
Function Notation
f(x) = 4x + 8
g(x) = -7x + 5
h(x) = 5x – 7

9. Evaluating a Function Find each function value for f(x) = 4x + 8
Given g(x) = -7x + 5; find g(2)
g(2) = -7(2) + 5
g(2) =
g(2) = -9

10. You can read 2000 words in 8 minutes.
Evaluating a function
The function w(x) = 250x represents the number of words w(x) you can read in x minutes. How many words can you read in 8 min?
w( ) = 250( )
w(x) = 250x
w(x) = 250x 8 8
Assignment:
pg 271 ( 1-3, 8-17,
26,27,31-34)
w( 8 ) = 2000
What does w(8) = 2000 mean?
You can read 2000 words in 8 minutes.

11. assignment
pg 271 ( 1-3, 8-17,26,27,31-34)