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 $x$.