https://file.aiquickdraw.com/mathbot/file/1727359556833fjsh2q2s.jpg

give answers according to the question options.

Let's go through each statement to determine which ones are true for functions:

1. **All functions have a dependent variable.**
   - **True**: In a function, one variable (the dependent variable) depends on the other (the independent variable).

2. **All functions have an independent variable.**
   - **True**: A function requires an independent variable, which is the input for the function.

3. **The range of a function includes its domain.**
   - **False**: The domain is the set of all possible input values, while the range is the set of all possible output values. These are separate concepts; the range doesn't include the domain.

4. **A vertical line is an example of a functional relationship.**
   - **False**: A vertical line fails the vertical line test for functions because it associates one input with multiple outputs.

5. **A horizontal line is an example of a functional relationship.**
   - **True**: A horizontal line passes the vertical line test, so it is a function.

6. **Each output value of a function can correspond to only one input value.**
   - **False**: This describes a one-to-one function, but not all functions are one-to-one. Some functions allow multiple inputs to have the same output.

### Summary of answers:
- **True**: Statements 1, 2, 5
- **False**: Statements 3, 4, 6

Would you like more details on any of these points?

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Here are five related questions to expand your understanding:
1. What is the vertical line test, and how does it determine if a relation is a function?
2. Can a function have the same output for different input values?
3. How is the domain of a function different from its range?
4. What is an example of a one-to-one function?
5. How does a horizontal line function differ from a non-horizontal linear function?

**Tip**: Remember that the **domain** of a function is the set of all input values, and the **range** is the set of all output values.

Which statements are true of functions? Check all that apply.

Explore key concepts of functions, including dependent and independent variables, domain and range, and the vertical line test. Learn which statements about functions are true, covering algebraic relationships suitable for students in Grades 9-11.

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