Question

Vocabulary Terms - Define/Illustrate

Input
Output
Function

Answer 1

They're all mathematical terms

Answer 2

### Vocabulary Terms

1. **Input**
- **Definition**: Input refers to the data or information that is sent into a system or process for processing. In the context of computing, input can be any signal or data entered into a computer system for processing, such as keyboard strokes, mouse clicks, or data from sensors.
- **Illustration**:
- From a user perspective, when you type "Hello" into a chat application, "Hello" is the input.
- In programming, if you have a function that takes numerical values, the numbers you provide to the function are considered the input.

2. **Output**
- **Definition**: Output is the result produced by a system after processing the input. It can be any form of data or information that is emitted from a system, like text displayed on a screen, data written to a file, or results sent to another device.
- **Illustration**:
- Continuing with the chat application example, if the application responds with "Hi there!", that response is the output.
- In programming, if a function takes two numbers as input and returns their sum, the sum produced by the function is the output.

3. **Function**
- **Definition**: A function is a reusable block of code designed to perform a specific task. In mathematics, it describes a relationship between a set of inputs and an output. In programming, functions accept input (arguments), perform operations on that input, and return an output.
- **Illustration**:
- In a mathematical context, a function \( f(x) = x^2 \) takes an input \( x \) and outputs \( x \) squared. For instance, if \( x = 3 \), then \( f(3) = 9 \).
- In programming, a simple Python example would be:
```python
def add_numbers(a, b):
return a + b
```
Here, `add_numbers` is a function that takes two inputs (a and b), adds them, and returns the output. For example, `add_numbers(2, 3)` outputs `5`.

Answer 3

Certainly! Here's a definition and illustration of the terms "input," "output," and "function," specifically in the context of mathematics:

### Mathematical Vocabulary Terms

1. **Input**
- **Definition**: In mathematics, an input refers to the value or values that are fed into a function. It is the independent variable upon which the function operates.
- **Illustration**: In the function \( f(x) = 2x + 3 \), if we provide \( x = 4 \) as the input, it can be represented as:
\[ f(4) = 2(4) + 3 \]
Here, \( 4 \) is the input.

2. **Output**
- **Definition**: Output is the result produced by a function after processing the input. It is the dependent variable that results from the function's operation on the input.
- **Illustration**: Continuing with the above function \( f(x) = 2x + 3 \), if we use the input \( x = 4 \), we calculate:
\[ f(4) = 2(4) + 3 = 8 + 3 = 11 \]
Hence, \( 11 \) is the output of the function for the input \( 4 \).

3. **Function**
- **Definition**: A function is a mathematical relation that assigns exactly one output for each input from a specified set. It can be represented in various forms, including equations, graphs, or algorithms.
- **Illustration**:
- An example of a function is \( f(x) = x^2 \), which takes an input \( x \) and provides the square of that number as output.
- For example, if the input is \( 3 \):
\[
f(3) = 3^2 = 9
\]
- This shows a function mapping each input \( x \) to an output \( f(x) \).

### Summary
In a mathematical context, inputs are the values you give to a function, outputs are the results you get back after processing those inputs, and a function is the rule or relationship that describes how each input is transformed into an output.