Back To Course

Math 101: College Algebra12 chapters | 95 lessons | 11 flashcard sets

Are you a student or a teacher?

Start Your Free Trial To Continue Watching

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.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Luke Winspur*

Luke has taught high school algebra and geometry, college calculus, and has a master's degree in education.

Adding, subtracting, multiplying and dividing functions is about as simple as substituting in expressions and then just doing whichever operation it asks you to do. Check out this video lesson to see some examples of this and learn just how easy it is!

I'm a pretty big sports fan, but I've always been bummed out by how expensive it is to buy gear from my favorite teams. But when I recently moved to Minneapolis, I made some friends that have decided to do something about it! They just opened their own t-shirt company called Tinyapolis that sells t-shirts for the popular teams here in Minnesota.

But when you own your own business, you want to be sure that you're going to be able to make money. So before they took the plunge and bought all the supplies to begin making their shirts, they figured out what their **revenue function**, or **r(x)**, would be. This is the function that would tell them how much money they would make from selling *x* t-shirts. But it's just as important to know what the **cost function**, or **c(x)**, would be. This would tell them how much money they would have to spend in order to make *x* t-shirts.

After doing a little research, they came up with the revenue and cost functions seen here: r(*x*) = 20*x* and c(*x*) = *x*2 - 1100*x* + 1200. But separate, these two functions don't tell the whole story. What is most important is, after it is all said and done and the t-shirts have been made and sold, did they make money or lose money?

That's where the **profit function**, or **p(x)**, comes in. The profit function would tell my friends whether they would make more money from selling the shirts than it would cost them to make them. This means that the profit function is simply the revenue function minus the cost function. If it costs more to make *x* t-shirts than they make from selling them, they'll have negative profit. But if they make more from the sales than they spend producing the shirts, they'll be in good shape!

So what does this profit function actually look like? Well, all we really have to do is substitute in what we already know the revenue and cost functions are and then simplify. First we'll go ahead and distribute the negative sign to the *x*2, the -1100*x* and the 1200. Then we combine like terms by grouping together the 20*x* and the 1100*x*, and we end up with our profit function as this: p(*x*) = -*x*2 + 1120*x* - 1200. Whoa, if those numbers are correct, they're going to be rolling in it. I hope they spread the wealth!

This was an example of a **function operation** - specifically, subtraction. But we can do all the major operations on functions, such as addition, multiplication and division. All of these different operations simply require you to substitute in what you know the function is and go from there, which really isn't too bad, but there are a few reasons that these problems can get tricky.

First, just the function notation itself often confuses people into thinking it's more difficult than it actually is. Secondly, there is a good amount of prerequisite knowledge you need to know in order to fully solve function operation questions. This is because each operation will end up asking you to do something a little different. For example, when we subtracted functions just a few seconds ago, we were required to combine like terms. But when you multiply functions, you'll often have to remember how to multiply polynomials with FOIL or the area method. But that means as long as you're comfortable with function notation and have a solid algebra background, there isn't anything to it.

Let's take a look at a different example that will ask us to use a different operation, maybe multiplication like I just mentioned. If f(*x*) = *x*2 + 2*x* - 5 and g(*x*) = 3*x* - 1, then what is f(*x*) * g(*x*)?

Let's avoid the first pitfall and not let all this function notation freak us out. All we're being asked to do is multiply the two functions, so we can substitute in those expressions they listed for us like this. At this point, it's simply a matter of using our algebra skills to simplify the expression. Because we're multiplying polynomials, that means FOIL-type multiplying. Basically, we need to multiply each term from this front expression with each term in the second one.

I like using the area method to organize my work for multiplying polynomials that have more than two terms. That requires us to make a chart that has dimensions equal to the number of terms in our two polynomials - in this case, three by two. Next, we label the top and the side of the chart with our two polynomials. So the top, which is divided into three sections, gets f(*x*) (*x*2, 2*x* and -5), while the left of the chart gets g(*x*) (3*x* and -1). Now we fill in the chart by multiplying the terms to the left and above each box. For example, the first box will be *x*2 * 3*x* = 3*x*3. Continuing this process would look like this, and now we just combine whatever like terms we have to find our final answer is 3*x*3 + 5*x*2 - 17*x* + 5.

Dividing functions is a very similar process. We won't have to multiply with the area method, but we'll still substitute in expressions and simplify whatever we're left with. Let's try this example: given g(*x*) = 4*x*5 and h(*x*) = 8*x*2, what is g(*x*) / h(*x*)?

Don't worry about the notation; let's just substitute in what we know g and h are. That leaves us with this: 4*x*5 / 8*x*2. Now we just need to simplify our expression, this time with our exponent properties.

We can either use the quotient of powers property, which tells us to subtract the exponents, or we can simply write out the *x*s we've got and cancel out any that are on the top and the bottom. Either way, we should end up with only three *x*s left in the numerator. Now we can simplify the numbers using middle school simplifying of fractions skills to say that 4/8 is the same as 1/2, and we've got our answer: *x*(3/2)!

We can add, subtract, multiply or divide functions by substituting in what we know the function is and then simplifying the expression. These things are called function operations. The key to function operations is to not let the function notation get you off track. Substitute in what you know the functions are, and then use whatever algebra knowledge you have to simplify the expression.

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

BackDid 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
4 in chapter 7 of the course:

Back To Course

Math 101: College Algebra12 chapters | 95 lessons | 11 flashcard sets

- Functions: Identification, Notation & Practice Problems 9:24
- Transformations: How to Shift Graphs on a Plane 7:12
- What Is Domain and Range in a Function? 8:32
- How to Add, Subtract, Multiply and Divide Functions 6:43
- Inverse Functions 6:05
- Applying Function Operations Practice Problems 5:17
- Go to Functions

- GRE Information Guide
- Computer Science 310: Current Trends in Computer Science & IT
- Earth Science 105: Introduction to Oceanography
- Computer Science 331: Cybersecurity Risk Analysis Management
- Computer Science 336: Network Forensics
- Practical Applications for Excel
- Practical Applications in Business Law
- Practical Applications for How to Network
- Practical Application for Technical Writing
- Practical Applications for Workplace Communications with Computers
- Study.com Grant for Teachers
- What are the MEGA Tests?
- MOGEA Test Score Information
- ASWB Prep Product Comparison
- What is the MOGEA Test?
- TASC Exam Registration Information
- How to Study for the TASC Exam

- Marginal Value in Economics: Definition & Theorem
- Teaching Reading Fluency to Improve Reading Comprehension
- Using Technology in the History Classroom
- Health Services: Definition, Types & Providers
- Dr. Seuss Political Cartoon Lesson Plan
- Practical Application: Developing a Thesis Statement from Your Speech Topic
- EMTALA: Definition, Requirements & Example
- Practical Application: Basic Graphic Design Elements Infographic
- Quiz & Worksheet - Types of Communication Software
- Quiz & Worksheet - Hatchet Synopsis
- Quiz & Worksheet - Flow of Charge
- Quiz & Worksheet - Citing Textbooks in MLA
- Quiz & Worksheet - Finding Area from Diameter
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies

- Holt McDougal Introduction to Geography: Online Textbook Help
- Guide to Career Planning and Development
- MTLE Health: Practice & Study Guide
- How to be an Effective Manager
- Macroeconomics Textbook
- PLACE Mathematics: Graphing Derivatives & L'Hopital's Rule
- NMTA Essential Academic Skills Math: Discrete Math
- Quiz & Worksheet - Finding the F-Ratio
- Quiz & Worksheet - Point of View in Death of a Salesman
- Endangerment of Polar Bears: Quiz & Worksheet for Kids
- Quiz & Worksheet - Barilla SpA SCM Case Study
- Quiz & Worksheet - Perceptual Motor Development

- Quantifiers in Mathematical Logic: Types, Notation & Examples
- Using Comics in the Classroom
- Georgia Biology Standards
- Best GMAT Prep Book
- Is PHP Hard to Learn?
- Understanding TELPAS Scores
- Next Generation Science Standards for Middle School
- Cool Science Facts
- Scientific Method Experiments for Kids
- 504 Plans in Florida
- AP Macroeconomics Exam: Tips for Long Free-Response Questions
- 504 Plans in Florida

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

Browse by subject