1. Writing a Function Rule
Write a function rule for situation
C is 8 more than half of n.
2.5 more than the quotient of h and 3 is w.
y is 2 less than the product of 7 and x.

2. More Writing a Function Rule
Write a function rule for situation
The total distance d traveled after n hours at a constant speed of 45 miles per hour.
A worker’s earnings e for n hours when the worker’s hourly wage is $6.37.
The volume V of a cube when you know the length n of a side.
Suppose a plumber gets paid $60 for traveling time to a job plus $115 for each hour he takes to complete the job. The plumber charges for whole-number hours.

3. Even More Writing Function Rules
Suppose you borrow money from a relative to buy a lawn mower for $245. You charge $18 to mow a lawn. Write a rule to describe your profit P as a function of the number of lawns mowed n. If you mow 3 lawns a day Monday through Friday, how much profit will you make?
At a supermarket salad bar, the price of a salad depends on its weight. The salad costs $.05 for the container plus $.18 per ounce.
a) Write a rule to describe the function.
b) How much would a 9 ounce salad cost?

4. Definition of a Function
A function is a set of ordered pairs in which no two ordered pairs of the form (x, y) have the same x-value with different y-values.
That sounds easy enough. Maybe we should look at some examples.
Example 1
This is a function because there are no repeating x-values.
(-3, 9) (-2, 4) (-1, 1) (0, 0) (1, 1) (2, 2) (3, 3)
Example 2
This is not a function because there are repeating x-values.
(5, 7) (3, 5) (1, 4) (0, 0) (1, 6) (4, 2) (6, 3)
Example 2 is a relation.
That was easy

5. Mapping Diagrams That was easy
Make mapping diagrams for each of the following relations. Then determine if the relation is a function.
(0, 2) (1, 3) (2, 4)
(-1, -2) (3, 6) (-5, -10) (3, 2)
(-2, 8) (-1, 5) (0, 8)
(-1, 3) (2, 3)
(0, 2) (1, 4) (2, 6)
(3, 4) (4, 2) 1 2 2 3 4 -5 -1 3
-10 -2 2 6 1 2 3 4 2 4 6 -2 -1 2 3 5 8
Is a Function
Not a Function
Not a Function
Is a Function
That was easy

6. Vertical Line Test
A graph represents a function if any vertical line drawn intersects it in at most one point.
The vertical line never intersects the graph in more than one point, therefore this is a function.
The vertical line never intersects the graph in more than one point, therefore this is a function.
The vertical line does intersect the graph in more than one point, therefore this is not a function.

7. Applying the Vertical Line Test
Use the vertical line test to determine whether each relation is a function.
Asi De Facil
(-4, -2) (-2, 1) (-1, 4)
(2, 1) (4, -3)
(-4, -4) (-4, 2) (0, 1)
(2, 4) (4, -4)
(-3, 1) (-1, -3) (-1, -1)
(-1, 1) (2, 2) (2, 4) 4 2 -2 -4 4 2 -2 -4 4 2 -2 -4
The vertical line never intersects the graph in more than one point, therefore this is a function.
The vertical line does intersect the graph in more than one point, therefore this is not a function.
The vertical line does intersect the graph in more than one point, therefore this is not a function.

8. Do Not Identify Domain & Range
Homework
Page 265: 8 – 20 Even Numbers
Volume of a Cylinder =
Page 271: All Questions
Do Not Identify Domain & Range

9. Function Notation x = y = f(x) =
For any function f, the notation f(x) is read “ f of x” and represents the value of y when x is replaced by the number or expression inside the parenthesis.
Input Value
Independent Variable
x =
Domain
y =
f(x) =
Output Value
Dependent Variable
Range
Domain
Set of all independent variables for which a function is defined.
All x-values.
Range
Set of all dependent variables for which a function is defined.
All values of f(x).

10. Making a Table for a Function
Make a table for the function using the following domain. {0, 1, 2, 3, 4} x -3 1 2 3 4 -1 1 3 5
That was easy

11. Finding Domain and Range
Write the ordered pairs for the relation shown in the graph and find the domain and range for each example. 4 2 -2 -4 4 2 -2 -4 4 2 -2 -4
(-4, -2) (-2, 1) (-1, 4)
(2, 1) (4, -3)
(-4, -4) (-4, 2) (0, 1)
(2, 4) (4, -4)
(-3, 1) (-1, -3) (-1, -1)
(-1, 1) (2, 2) (2, 4)
Domain {-4, -2, -1, 2, 4}
Domain {-4, 0, 2, 4}
Domain {-3, -1, 2}
Range {-3, -1, 1, 2, 4}
Range {-3, -2, 1, 4}
Range {-4, 1, 2, 4, }
Asi De Facil

12. Finding the Range for a Given Domain
Find the range of each function for the domain x
f(x) x
f(x) x
f(x) -2
0.7
2.3 -7 -2
0.7
2.3 8 -2
0.7
2.3 3
-1.6
-0.1
-4.02
1.6
-4.9
5.58
Range {-7, -1.6, 1.6}
Range {8, -0.1, -4.9}
Range {3, -4.02, 5.58}
That was easy
Asi de facil

13. Using a Table to Represent Functions
Determine if each relation is a function and if so state the domain and the range. x y x
f(x) x
f(x) 1 2 3 4 3 5 7 9 -3 5 6 2 4 -1 2 7 11 14 2 7 11 14
Yes
Domain {1, 2, 3, 4} No
Yes
Domain {2, 7, 11, 14}
Range {3, 5, 7, 9}
Range {2, 7, 11, 14} x
f(x) x y x y 2 5 -1 -4 -8 -7 -2 -1 1 3 5 -6 4 -1 -2 1 2 3 4 No
Yes
Domain {-2, -1, 0, 1} No
Range {3, 5, -6, 4}

14. Identify Domain & Range Only
Homework
Page 271: 8 – 11
Identify Domain & Range Only
Page 272: 18, 20, 24, 25