How to Interpret the Parameters of a Linear Function | Mathematics
Now that you have a comprehensive understanding of various types of functions and their processes, ranging from:
- The domain and range of functions
- Finding the minimum and maximum of quadratic functions
- Graphing quadratic functions
- Graphing linear functions
- Graphing exponential functions
You can take your skills a step further in preparation for the TASC Test Assessing Secondary Completion™. Today we will learn how to interpret the parameters of a linear function.
What is a parameter?
You previously learned that in their simplest form, linear functions can be written as y = f(x) = ax. They can also be written in the form of y = a + bx, where a and b are given different values. These constants are called parameters.
According to mathematician Dr. William Mueller, parameter a is the function's y-intercept, and parameter b is the slope.
Although we won’t be graphing parameters today, it’s important you know what they are and how to find them. The real-life example below will show you how to find a linear function’s parameters, and assess your growing knowledge of functions.
Example: Finding and Interpreting Linear Function Parameters
A youth ski team formed last winter at Copper Mountain Ski Resort in Colorado. The kick off season was successful, but the team didn’t hit its membership goal of 500 members.
Last winter’s membership can be shown by the function: y = 350 + 25x, where:
- y represents the total number of members
- 350 represents the number of members who joined last year
- 25 represents the number of members joining each week
- x represents the number of weeks
From the information above, let’s solve the following problems:
- What are the function’s parameters?
- After how many weeks will the ski team reach full membership?
- What is the domain and range of the function?
- If the number of members who joined each week increased to 50, how would the function change?
- How would the parameters change?
Solutions:
- Identify what parameter a and b align to in the function: y = 350 + 25x.
The parameters are: a = 350 and b = 25.
- Make a table to figure out how many weeks it will take the ski team to reach its membership goal of 500 using the function: y = 350 + 25x.
Weeks |
Members |
2 |
350 + 25 (2) = 400 |
3 |
350 + 25 (3) = 425 |
4 |
350 + 25 (4) = 450 |
5 |
350 + 25 (5) = 475 |
6 |
350 + 25 (6) = 500 |
It will take the ski team six weeks to acquire 500 members at a rate of 25 new members per week.
- Take a look at a previous TASC test blog post detailing how to find the domain and range of functions. The function’s domain and range can be expressed as:
Domain: {0 ≤ x ≤ 6}
Range: {350 ≤ y ≤ 500}
- The number of members who join each week affects the rate of change – increasing from 25 to 50 members per week. The new function is: y = 350 + 50x. By making a new table, we see that in just three weeks the ski club will hit its goal of 500 members.
Weeks Members 2
350 + 50 (2) = 450
3
350 + 50 (3) = 500
- In the new function of y = 350 + 50x, the parameters are: a = 350 and b = 50. The change in parameters would only affect the domain (slope of the function):
Domain: {0 ≤ x ≤ 3}
Range: {350 ≤ y ≤ 500}
Regardless of the join rate per week, the domain and range are restricted due to the club’s maximum member capacity of 500 members (y-intercept).
This example was modified from a lesson created by Sarah Peterson on LearnZillion. Want to learn more? Continue your understanding of parameters with exponential functions.