give an example of a function, and an example of a non-fuction

### Example of a Function:
Consider the relation \( f(x) = 2x + 3 \). 

In this case, for every input \( x \), there is a unique output. For example:
- If \( x = 1 \), then \( f(1) = 2(1) + 3 = 5 \).
- If \( x = 2 \), then \( f(2) = 2(2) + 3 = 7 \).

Here, each input \( x \) produces exactly one output, so this relation is a function.

### Example of a Non-Function:
Consider the relation \( y^2 = x \).

In this case, if you input \( x = 4 \), there are two possible outputs for \( y \):
- \( y = 2 \), because \( 2^2 = 4 \)
- \( y = -2 \), because \( (-2)^2 = 4 \)

Since a single input \( x = 4 \) leads to two different outputs (\( y = 2 \) and \( y = -2 \)), this relation is not a function.

Would you like more details or have any questions?

Here are 5 related questions you might find helpful:
1. How can you express a function using a graph?
2. What is the importance of the vertical line test in determining a function?
3. How do you define the domain and range for the function \( f(x) = 2x + 3 \)?
4. Can a quadratic equation like \( y = x^2 \) be a function? Why?
5. How do you determine if an equation represents a function without graphing?

**Tip:** Remember, in a function, each input corresponds to exactly one output, but different inputs can share the same output.

Explore examples of functions and non-functions in mathematics with detailed explanations. Learn about the criteria that define a function and encounter scenarios where relationships do not meet these criteria. Suitable for Grades 7-9 students and anyone interested in understanding fundamental concepts in algebra.

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