5-4: Writing Function Rules
Objective:
• You will be able to write an equation for a table.
• You will be able to write an equation for a real­world situation.
Review:
function
rule
related
A _____________ ________ shows how your variables are _____________.
equation
(We commonly call a function rule an ___________________.)
Key Question:
To determine what a function rule is, ask yourself the key question:
"What am I doing to x to get y?"
Definitions:
independent
The x­variable is called the __________________________ variable.
(This is because we can choose any number we want for x to put into the equation – its value is not dependent on anything.)
dependent
The y­variable is called the ______________________ variable.
(This is because we have to calculate the value for y – its value depends on what we choose for x.)
Examples:
Write a function rule for each table.
1.
2.
For some rules, there are different ways of writing the same thing... we want to simplify the equation (rule) whenever possible.
REMEMBER: Ask yourself "What am I doing to x to get y?"
REMEMBER: Ask yourself "What am I doing to x to get y?"
3.
4.
5.
6.
Remember, we can use addition, subtraction, multiplication, division, squares and square roots... OR a combination of any of these operations when creating a rule!
This one is not in your notes...
Real World Examples:
Given the situations below, write a function rule then answer the question asked.
The Museum of Science in Boston, MA has an exhibit called The Walk Through Computer 2000. It is a scale model of a desktop computer. It is about 20 times the size of a normal­sized desktop computer.
TM
a.
Write a function rule to describe the relationship between the normal sized computer and the size of the exhibit.
b.
A space bar on a normal­sized computer is 4 3/8 " long. About how long is the space bar in the exhibit?
7.
A carpenter buys finishing nails by the pound. Each pound of nails costs $1.19.
a.
Write a function rule (equation) to describe the relationship between cost and number of pounds of nails.
b.
How much would it cost to purchase 12 lbs. of finishing nails?
8.
Suppose you borrow money from a relative to buy a lawn mower that costs $245. You charge $18 to mow a lawn.
a.
How much money do you have when you start your business?
b.
How can you represent the income you gain each time you mow someone’s lawn?
c.
Write a function rule (equation) by putting your answers in parts (a) and (b) together to show your income.
d.
Use your equation in part (c) to calculate whether or not you would be finished paying your relative back if you mowed 20 lawns.
9.
Suppose you buy a word­processing software package for $199. You charge $15 per hour to type papers for other students.
a.
How much money do you have when you start your business?
b.
How can you represent your income to show how much you charge per hour?
c.
Write a function rule (equation) by putting your answers in parts (a) and (b) together to show your income.
d.
Use your equation in part (c) to calculate your profit after typing for 24 hours.
e.
Use your equation in part (c) to calculate your profit after typing for 10 hours. What does this mean? Tonight's homework:
The worksheet packet handed out in class.
(...and any other homeworks not yet done for Chapter 5)