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 2

2. 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

3. 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)

4. 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

5. Find the range of the function for the given domain.
The domain of f(x) = 4x - 12 is {1,3,5,7,9}. What is the range? (use a table) x
4x - 12
f(x) 1
4( ) - 12 1 -8 3
4( ) - 12 3 5
4(5 ) - 12 8 7
4( 7) - 12 16 9
4( 9) - 12 24
What is the range?
{-8, 0, 8, 16, 24}

6. f(x) = -1.5x + 4 f(1) = -1.5(1)+ 4 f(1) = = 2.5 Pg 271: 3-5, 18-21
The domain of f(x) = -1.5x + 4 is {1,2,3,4}. What is the range?
Use function notation
f(x) = -1.5x + 4
f(1) = -1.5(1)+ 4
f(1) =
= 2.5
Pg 271:
3-5, 18-21
f(2) =
f(2) = -1.5(2)+ 4
= 1
f(3) =
f(3) = -1.5(3)+ 4
= -.5
f(4) = -1.5(4)+ 4
f(4) =
= -2
The range is:
{-2, -.5, 1, 2.5}

7. 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(x) = 250x
w( ) = 250( )
w(x) = 250x 8 8
w( 8 ) = 2000
What does w(8) = 2000 mean?
You can read 2000 words in 8 minutes.

8. 0 < q < 3 q 3 0 < A(q) < 300 A(q) A(0) = 100(0)
You have 3 qt of paint to paint the trim in your home. A quart of paint covers 100ft2. The function A(q) = 100q represent the area A(q), in square feet, that q quarts of paint cover. What domain and range are reasonable for the function? What is the graph of the function?
KNOW NEED PLAN
Have 3 qt of paint
Reasonable domain and range values
Find least and greatest amounts of paint. Make a graph.
1 qt covers 100ft2
Domain:
variable?
Smallest amount? Largest amount?
0 < q < 3 q 3
Range:
variable?
Smallest amount? Largest amount?
0 < A(q) < 300
A(q)
A(0) = 100(0)
A(3) = 100(3)
A(0) = 0
A(3) = 300
Paint usage q
A(q) 1 2 3
300
200
100
Area
100
page 271: 4,5,
18-24, 28,29
200
300
Paint used (qt) q

9. Assignment: pg 271 ( 3, 16-21,26,27,31-34,41)