# Determine the Initial Value of a Function

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• 0:01 Initial Value of a Function
• 2:25 Mathematical Examples
• 4:15 Lesson Summary

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Lesson Transcript
Instructor: John Sepanski

John has taught 6th Grade Mathematics through Geometry and has a Master's degree in Education

In this lesson, you will learn to determine the initial value of a function by studying functions in the form of word problems, graphs and linear equations.

## Initial Value of a Function

Almost everybody today has a cell phone. Some people have very basic phones; others have their brothers' and sisters' old phones; some people have really beat-up phones! Well, pretty soon, that one big computer company will be releasing the latest and greatest new phone and everybody's going to want one, especially me!

But in order to afford that new phone, I'm going to have to sign a contract. A contract is a document that says you can get the new phone for a special price as long as you agree to stay with the cellular company for two years and make monthly payments for your data usage, texts and calls. This is a great example of the initial value of a function.

The initial value of a function is the point at which a function begins. Well, that makes sense, but what does it really mean? A function is a mathematical relation into which we input values of a domain that generate output values of a range. Let's take a step back to our phone example to help break this concept down a little.

Suppose that when it's released, the cost of the latest, greatest, coolest phone is \$650, but you can get it for only \$200 as long as you're willing to sign a contract. That contract is going to include your agreement to a two-year agreement with a plan including voice, data and text. Hang on a minute. All those words mean that your phone isn't really going to cost you just \$200. It means that you start by paying \$200, but then you pay an amount, say \$110, every month for two years.

Your initial value was just the beginning! Your phone actually will cost you \$2,840 over the time of two years. I wonder if I can buy the phone without a contract? It will probably cost a lot more, but it might be worth it, but then I would have to pay for data anyways.

## Mathematical Examples

Let's take a look at some strictly mathematical functions. Consider the example f(x) = 2x + 10.

Maybe you could think of this standing for the cost of riding rides at a carnival. It costs \$10 to get in, but it will cost you \$2 more for every ride you get on. In this case, the initial value of the function is 10. In other words, if you ride 0 rides and just go to the fair, it will cost you \$10.

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