1. 5-4: Writing a Function Rule
This lesson has two parts:
Look at a table of values, find a pattern, and write the function rule (equation) that describes the pattern.
Translate a real world problem into a function rule (equation).

2. Look for the pattern and write the function rule.x y 1 5 2 6 3 7 4 8
y = something done to the x.
5 =
Something done to 1.
1 + 4…does this work for the other x’s?
y = x + 4
6 =
7 = 3+ 4
8 =
YES!
y = x + 4 is the function rule!

3. Look for the pattern and write the function rule.x y 1 3 9 6 36 81
y = something done to the x.
1 =
Something done to 1.
12…does this work for the other x’s?
y = x2
9 = 32
36 = 62
81 = 92
YES!
y = x2 is the function rule!

4. Writing a Function Rule
ALGEBRA 1 LESSON 5-4
Write a function rule for each table. x
ƒ(x) 2 8 4 10 6 12 14
ƒ(x) = something done to the x.
8 =
Something done to 2.
2 +6…does this work for the other x’s?
y = x + 6
10 =
12 =
14 =
YES!
y = x + 6 is the function rule!

5. Writing a Function Rule
ALGEBRA 1 LESSON 5-4
(continued)
You try one! b.
x y
1 2
2 5
3 10
4 17
2 = something done to 1
5 = something done to 2
10 = something done to 3
Relate:    equals plus 1
Write: = x2 y
x times itself
A rule for the function is y = x2 + 1.

6. Writing a Function Rule
ALGEBRA 1 LESSON 5-4
The journalism class makes $25 per page of advertising in the yearbook. If the class sells n pages, how much money will it earn?
a. Write a function rule to describe this relationship.
Relate:    is  25  times  
money earned
number of pages sold
Define: Let = number of pages sold. n
Let = money earned. y
Write: = 25 •
The function rule y = 25n describes the relationship between the number of pages sold and the money earned.

7. Writing a Function Rule
ALGEBRA 1 LESSON 5-4
(continued)
b. The class sold 6 pages of advertising. How much money did the class make?
y = 25 • 6 Substitute 6 for n.
y = 150 Simplify.
y = 25 • n
The class made $150.

8. Writing a Function Rule
The choir spent $100 producing audio tapes of its last performance and will sell the tapes for $5.50 each. Write a rule to describe the choir’s profit as a function of the number of tapes sold.
Profit = selling price - cost
Relate: is $5.50 times minus cost of tape production
total profit
tapes sold
Define: Let = number of tapes sold. t
Let = total profit. y
Write: = • – 100
The function rule y = 5.5t – 100 describes the profit as a function of the number of tapes sold.

9. Extra Practice 1. Write a function rule for each table. x y –1 –5 0 0
ALGEBRA 1 LESSON 5-4
1. Write a function rule for each table.
x y
–1 –5
0 0
1 5
2 10 a.
x ƒ(x)
–1 –4
0 –3
1 –2
2 –1 b.
y = 5x
ƒ(x) = x – 3
2. Write a function rule to describe each relationship.
a. the total cost T(c) of c pounds of apples at $.82 a pound
b. a scale model s of a moth m that is 6 times the actual size of the moth
y = 0.82c
y = 6m
3. You borrow $60 to buy a bread-making machine. You charge customers $1.50 a loaf for your special bread. Write a rule to describe your profit as a function of the number n of loaves sold.
y = 1.5n - 60