### The domain and range of this function can be represented mathematically as follows:

*October 10, 2022*

**Review the assigned reading, paying particularly close attention to “Why It Matters: Functions and Function Notation,” and “Lesson 8: Functions and Their Notation.” Additionally, you may find it helpful to complete the Lesson 8 Homework to prepare for this discussion.**

**From this week’s reading, we learn that a** **relationis a correspondence between an input value and an output value. Moreover, a** **function** **is a relation in which every input value corresponds to** **only oneoutput value.**

**Relations and functions come in many different forms, and many real-life concepts can be thought of in terms of relations or functions. Consider a snack vending machine, for instance. To purchase a snack, you must press buttons (input) that correspond to your desired snack (output). If you press “A1”, you may receive Peanut M&Ms. If you press “A2”, you may be the recipient of a Snickers bar. “A3” might be a bag of Barbecue Chips.**

**This relation between vending machine buttons and snacks that are described above can be represented by a function since every button (input value) corresponds to** **only one** **output value (snack). I could represent this** **function using function notation. Let** **S****=** **f****(****b****) be a function that identifies the snack,** **S****, from a vending machine when a button,** **b****, is pushed. Using function notation, this can be written as** **f****(****A1****) = Peanut M&Ms,** **f****(****A2****) = Snickers,** **f****(****A3****) = Barbecue Chips, and so on.**

**The** **domain** **and** **range** **of this function can be represented mathematically as follows:**

**Domain = {A1, A2, A3, …}**

**Range = {Peanut M&Ms, Snickers, Barbecue Chips, …}**

**Note that as long as the vending machine is stocked such that every button corresponds to a single snack, the relation described above represents a function, because every input has only one output. However, if the vending machine is stocked randomly so that a variety of snacks (outputs) correspond to the same button (input), the relation no longer would represent a function. In this case, the first time that A1 is pressed, Peanut M&Ms may come out, and the second time A1 is pressed, a Kit Kat may come out. Then, f (A1) = Peanut M&Ms or f (A1) = Kit Kat. Since A1 is paired with more than one output, the relation would no longer represent a function.**

**Respond**

**Describe a real-life situation that can be modeled by a****function****(a relation in which every input value corresponds to****only one****output value). The situation must be different from the examples provided in the reading and in the homework. Identify the input value and the output value of the function, and provide justification that your relation does, in fact, represent a function.****Create a function in the form****y****=****f****(****x****) that models the relation described. You may choose variables in place of****y****or****x****that better represent the relation, as seen in the provided example.****Identify the domain and range of your function, using proper mathematical notation.****Cite any sources you may have used in formulating your response.**

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