Learn How To Write A Function Rule

This lesson is how to write a function rule. This video shows how functions typically behave, and how to write them down. Functions usually have a variable with a coefficient in front that represents the rate of change and has a constant value that represents the starting point of the function. After you finish this lesson, view all of our Algebra 1 lessons and practice problems.

The setup for this would look like:

Where # represents a constant
$y = (\#_1) x + (\#_2)$

$(\#_1)$ $\rightarrow$ the constant rate of change
$(\#_2)$ $\rightarrow$ the starting point, x = 0

Examples of Writing a Function Rule

Example 1

Jason goes to an amusement park where he pays $\$8$ admission and $\$2$ per ride. What is the function of the cost?

The cost is $2$ times the number of rides plus $8$ . This can be written as a function:

$y=2x+8$

Example 1

Maya has an internet service that currently has a monthly access fee of $\$11.95$ and a connection fee of $\$0.50$ per hour. Represent her monthly cost as a function of connection time.

The cost has two parts: the one-time fee of $\$11.95$ and the per-hour charge of $\$0.50$ . So the total cost is the charge per hour $\times$ the number of hours $+$ the flat fee

$y=0.50x+11.95$

Video-Lesson Transcript

We’re going to cover how to write a function rule for particularly linear functions.

Linear function has a basic form:

$y = (\#_1) x + (\#_2)$

Where the $(\#_1)$ represents the constant rate of change

and $(\#_2)$ is the starting point. The starting point is where $x = 0$ .

For example:

We have a cellphone plan that requests $\$25$ at sign up and requires $\$60$ per month. What is the function of the cost?

It will be cost equals $25$ start-up fee plus $60$ multiplied by the months.

So we’ll have

$c = 60m + 25$

This relates very closely with the basic form of linear equation which is $y = \#x + \#$ .

Let’s look at another example.

A bank account has $\$200$ in it. Every week, $\$20$ is added to it. Write a function to represent the amount of money (m) in the bank account after (w) weeks.