Back To Course

Common Core Math Grade 8 - Functions: Standards5 chapters | 19 lessons

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Login here for access

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Elizabeth Foster*

Elizabeth has been involved with tutoring since high school and has a B.A. in Classics.

Can you compare functions when they're written out numerically as tables of values? In this lesson, you'll learn to do just that and to compare one function as a table to another written in a different form.

When most people think about functions, they think about function notation and equations that start with *'F(x)*'. But *F(x)* is not actually what a function is; it's just one way to write a function. Conceptually, a **function** is a rule for transforming input values into output values. You have a certain range of input values, or *x*-values, that you can plug into the function. The function then tells you what you do to the *x*-values to transform them into output values, or *y*-values.

You can show functions in all kinds of ways, not just with function notation. Graphing is one alternative way, but you can also write a function numerically. A **function written numerically** is a table of values that shows the relationship between the inputs and the outputs of the function. Here's an example:

You can probably guess here that the function is *F(x)* = 2*x*, since all the output values in the *F(x)* column are the input values multiplied by 2.

In this lesson, you'll learn to compare functions written in tables either to other functions written in tables or to functions represented in some other way.

If you are given two functions represented in tables, you can compare important properties of the functions, like their rates of change. You can do this either by looking at the tables directly or by converting both functions into a form you find easier, like a graph. Here's an example:

*Given functions F and G, which function has the greater rate of change?*

In this example, you could look at the two functions and see just from the numbers that *G* is increasing more quickly: as *x* goes from 1 to 5, *F(x)* goes from 2 to 10, while *G(x)* goes from 3 to 15. For the same change in *x*, *F(x)* increases by 8, while *G(x)* increases by 12. Therefore, *G(x)* has a greater rate of change.

If that doesn't make sense to you, you could also use the values given in the tables to draw some quick graphs of the functions. From these graphs below, it's clear that *G(x)* has a steeper upward slope, so *G(x)* must have a faster rate of change than *F(x)*.

Sometimes, you'll also have to compare functions represented in two different forms. For example, you might have to compare the rate of change of a function written numerically in a table to a function drawn on a graph. Here's an example of that kind of comparison:

*Given the two functions F and G, which has a faster rate of change?*

Here, you could either convert *G(x)* into a table or convert *F(x)* into a graph. Pick your favorite method; there's no one right way to do it. If you showed them both as tables, your tables would look like this:

Comparing these tables, you can see that the rate of change is the same for both functions: for each function, *y* increases by 1 as *x* increases by 1. *G(x)* starts with a higher initial value, but don't get confused by this; the rate of change is the same.

Alternately, here's what it would look like if you showed them both as graphs:

Here, you can see that the lines are parallel, so their rate of change is the same. Again, don't get confused by *G(x)* having a higher initial value; this doesn't affect the rate of change.

In this lesson, you learned to compare the properties of **functions** when the **functions are expressed numerically** as a table of input and output values.

To compare two tables to each other, you can either look at the list of input and output values and draw conclusions from that, or you can convert them both to a form you find easier, like a graph. It all depends on what you're most comfortable with.

To compare a function expressed numerically to a function expressed some other way, just convert them both to the same form; again, you can pick whichever you prefer. Use whatever methods feel most comfortable to you. Now try some yourself on the quiz!

By completing this lesson, you should have the skills to:

- Explain how functions can be written numerically and shown in graphs
- Compare functions when one is written numerically and one is expressed differently

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Login here for access

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
3 in chapter 2 of the course:

Back To Course

Common Core Math Grade 8 - Functions: Standards5 chapters | 19 lessons

- Computer Science 109: Introduction to Programming
- Introduction to HTML & CSS
- Introduction to JavaScript
- Computer Science 332: Cybersecurity Policies and Management
- Introduction to SQL
- Algorithmic Analysis, Sorting & Searching
- Computer Programming Basics
- Stacks & Queues for Data Structures
- Functions & Modules in Programming
- Built-In Data Types for Programming
- CEOE Test Cost
- PHR Exam Registration Information
- Claiming a Tax Deduction for Your Study.com Teacher Edition
- What is the PHR Exam?
- Anti-Bullying Survey Finds Teachers Lack the Support They Need
- What is the ASCP Exam?
- ASCPI vs ASCP

- Multi-Dimensional Arrays in C Programming: Definition & Example
- Tests for Identifying Common Gases
- Speed, Velocity & Acceleration
- Functions & Parameters in C Programming
- Variable Scope in JavaScript: Explanation & Examples
- Family Tree Project Ideas for High School
- Random Numbers in JavaScript: Definition, Implementation & Examples
- Quiz & Worksheet - Average & Instantaneous Rates of Change
- Quiz & Worksheet - Incremental & Radical Change
- Quiz & Worksheet - Public Health vs. Medicine
- Quiz & Worksheet - Lion of the Tribe of Judah
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies
- Assessment in Schools | A Guide to Assessment Types
- 5th Grade Math Worksheets & Printables

- College Algebra Textbook
- AEPA Middle Grades Mathematics (NT203): Practice & Study Guide
- American Government: Help and Review
- Worth Publishers Psychology: Online Textbook Help
- Nervous System Study Guide
- NMTA Essential Academic Skills Math: Continuity
- MTTC Math (Secondary): Reasoning & Problem Solving
- Quiz & Worksheet - Influences on Emotional Expression & Their Impact on Communication
- Quiz & Worksheet - Literal, Inferential & Evaluative Meaning
- Quiz & Worksheet - Roots & Scientific Calculators
- Quiz & Worksheet - Development of Early Labor Arbitration
- Quiz & Worksheet - Evaluating the Reliability and Validity of Sources

- Pros & Cons of Going Global With a Business
- O'Brien in 1984: Character Analysis & Quotes
- Common Core State Standards in Oregon
- Weather Experiments for Kids
- Study.com's Guidance and Coaching Service
- Success Coaching with Study.com
- How to Pass the Series 6 Exam
- How to Use Study.com to Improve Your Grades
- FTCE Social Science 6-12: Passing Score
- How to Use Study.com in the Classroom
- NYS Earth Science Regents Exam Information
- Number Games for Kids

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject