The function \( P(x) = 2 \) is a constant function, meaning that for any input value of \( x \), the output is always \( 2 \). Here are some key points about this function:

1. **Domain:** The domain of \( P(x) \) is all real numbers, \( \mathbb{R} \), because \( x \) can be any real number.
2. **Range:** The range of \( P(x) \) is the single value \( \{2\} \), since \( P(x) = 2 \) for all \( x \).
3. **Graph:** The graph of \( P(x) = 2 \) is a horizontal line that crosses the y-axis at \( y = 2 \).
4. **Derivative:** The derivative of \( P(x) \) with respect to \( x \) is \( P'(x) = 0 \), since the function is constant and has no change as \( x \) changes.
5. **Integral:** The indefinite integral of \( P(x) = 2 \) is \( \int P(x) \, dx = 2x + C \), where \( C \) is the constant of integration.

Would you like more details on any of these points?

Here are 5 related questions you might find interesting:

1. What is the graph of a linear function compared to a constant function?
2. How does the derivative of a constant function differ from that of a linear function?
3. Can a constant function have any roots (zeros)?
4. How do you find the area under the curve of a constant function over a specific interval?
5. How does the integral of a constant function relate to its graph?

**Tip:** In calculus, the derivative of any constant function is always zero because a constant function does not change as the input changes.

Explore the constant function P(x) = 2, its domain, range, graph, derivative, and integral with a detailed explanation. Learn why the derivative of a constant function is always zero and how to integrate P(x) over different intervals. Ideal for high school students studying calculus.

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