**Which of the following is a function?**

A.)

B.)

C.)

D.)


To determine which of the given options is a function, we need more information about options A, B, C, and D. A function is defined as a relation where each input (or \(x\)-value) has exactly one output (or \(y\)-value).

Since the options were not provided, let's go over the general characteristics of a function and some examples to help identify a function from a list of options:

### Characteristics of a Function:
1. **Unique Outputs:** Each input value should map to exactly one output value.
2. **Vertical Line Test:** On a graph, if a vertical line intersects the graph at more than one point, the relation is not a function.

### Example Analysis:

#### Example 1:
Given a set of points:
- A: \((1, 2)\), \((2, 3)\), \((3, 4)\)
- B: \((1, 2)\), \((2, 3)\), \((1, 4)\)
- C: \(y = x + 1\)
- D: \(y^2 = x\)

- **Option A:** Each \(x\)-value corresponds to only one \(y\)-value. This is a function.
- **Option B:** The \(x\)-value 1 corresponds to two different \(y\)-values (2 and 4). This is not a function.
- **Option C:** The equation \(y = x + 1\) represents a line where each \(x\)-value has exactly one \(y\)-value. This is a function.
- **Option D:** The equation \(y^2 = x\) is a parabola that opens to the right. For a given \(x\)-value (except zero), there are two \(y\)-values (one positive and one negative). This is not a function.

Based on the examples:
- **A** and **C** are functions.
- **B** and **D** are not functions.

### Identifying Functions:
To determine which of the provided options (A, B, C, D) is a function, you need to check if each input has exactly one output.

Here are some steps and tips:
1. **Mapping Diagrams:** If the options are given as mapping diagrams, ensure that each input has a single arrow pointing to an output.
2. **Graph Analysis:** If graphs are provided, use the vertical line test.
3. **Equations:** Check the form of the equations. For example, \(y = mx + b\) (a linear equation) is always a function, while \(x = y^2\) is not because it does not pass the vertical line test.

Feel free to provide the specific options (A, B, C, D) for a precise determination.

Do you have any questions or need further details?

Here are 8 related questions to expand your understanding:

1. How can you determine if a graph represents a function using the vertical line test?
2. What are some common examples of functions and non-functions?
3. How do you use a mapping diagram to identify a function?
4. What is the difference between a relation and a function?
5. How can you determine if an equation represents a function?
6. What are one-to-one functions, and how do they differ from regular functions?
7. How can you find the domain and range of a function?
8. What are piecewise functions, and how do you analyze them?

**Tip:** Always ensure that each input value is paired with only one output value when identifying functions.

Learn how to identify functions from a set of options with examples and detailed explanations. Understand the characteristics of functions, including unique outputs and the vertical line test. Suitable for students in Grades 9-12.

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