Download 5-4: Writing a Function Rule

5-4: Writing a Function Rule
Objectives:
 You will write function rules to describe given situations.
 Given a table and/or graph of a function, you w ill write a function rule that describes that
function.
What’s my rule? Ask different students to give you numbers between 1 & 50, and tell them the
output. Then they must guess the rule.
1. f(x) = x + 2
2. f(x) = 2x
3. f(x) = 2x – 10
Writing a function rule from a situation
EX 1: Suppose you borrow money from a relative to buy a lawn mower that costs $245.You charge
$18 to mow a lawn. Write a rule to describe your profit as a function of the number of lawns mowed.
EX 2: Suppose you buy a word-processing software package for $199. You charge $15 per hour
for word processing. Write a rule to describe your profit as a function of the number of hours you
work.
EX 3: A zucchini plant in Keith’s garden was 10 centimeters tall when it was first planted. Since
then, it has grown approximately 0.5 cm per day.
a. Write a rule to describe the function.
H(d) = 0.5d + 10
b. When will the plant be 0.185 meters tall? After 17 days.
Writing a function rule from a table
 Ask yourself – “What can I do to x to make it equal f(x)?”
 Hint—Look at when x = 0, and at the change between x and y values.
Write a function for each table
EX 1: f(x) = x + 4
x
f(x)
0
4
1
5
2
6
3
7
4
8
EX 2: f(x) = -2x
x
f(x)
-2
4
-1
2
0
0
1
-2
2
-4
EX 3: f(x) = 0.5x
x
f(x)
0
0
1
0.5
2
1
3
1.5
4
2
EX 4: f(x) = -3x + 10
x
f(x)
-4
22
-3
19
-2
16
-1
13
0
10
EX 5: f(x) = 3x+1
x
f(x)
0
0
1
0.5
2
1
3
1.5
4
2
EX 5: f(x) = x2
x
f(x)
-4
16
-1
1
0
0
1
1
3
9
Writing a function rule from a graph
EX 1: f(x) = 3x
EX 2: f(x) = ½ x – 1