A table representing the function *f*(*x*) = 2 is shown below.

What is true of the given function?

The function increases at a constant additive rate.

The function increases at a constant multiplicative rate.

The function has an initial value of 0.

As each *x* value increases by 1, the *y* values increase by 1.\

For the given function \( f(x) = 2 \), let's analyze the options provided:

1. **The function increases at a constant additive rate.**
   - False. The function \( f(x) = 2 \) is a constant function, meaning that the value of \( f(x) \) remains the same (2) for all values of \( x \). There is no increase or decrease.

2. **The function increases at a constant multiplicative rate.**
   - False. Since the function is constant, there is no increase, multiplicative or otherwise.

3. **The function has an initial value of 0.**
   - False. The function always takes the value 2 for any \( x \), so it does not have an initial value of 0.

4. **As each \( x \) value increases by 1, the \( y \) values increase by 1.**
   - False. The \( y \) values (which represent \( f(x) \)) remain constant at 2 regardless of the changes in \( x \).

### Conclusion:
None of the provided statements are true for the given function \( f(x) = 2 \).

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Would you like more details, or do you have any questions? Here are some related questions to further expand on this:

1. What is the general form of a constant function?
2. How can we determine if a function is increasing or decreasing?
3. What does it mean for a function to increase at an additive rate?
4. What is the significance of an initial value in a function?
5. How do linear functions differ from constant functions?

**Tip**: A constant function always takes the same value, regardless of the input \( x \).

A table representing the function f(x) = 2 is shown below. What is true of the given function?

1. The function increases at a constant additive rate.
2. The function increases at a constant multiplicative rate.
3. The function has an initial value of 0.
4. As each x value increases by 1, the y values increase by 1.

Explore the properties of the constant function f(x) = 2. This problem breaks down why the function does not increase at a constant additive or multiplicative rate, does not have an initial value of 0, and why the y-values remain the same as x increases. Suitable for students in Grades 6-8.

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