The Constant Function: Properties, Graph, Derivative And Integral.

f(x)=c

f'(x)=0

The function f(x) = c is known as a constant function because it always returns the same value, c, for any input value of x. Here are some important properties of the constant function:

1. Domain: The domain of the constant function is all real numbers. In other words, you can plug in any value of x and get the same output, c.

2. Range: The range of the constant function is {c}. This means that the function only takes on one value, which is c.

3. Graph: The graph of the constant function is a horizontal line at the height of c. The line is parallel to the x-axis because the output never changes.

4. Derivative: The derivative of the constant function is zero. This is because the function has no slope – it is completely flat.

5. Integral: The integral of the constant function is simply the product of the value of the function and the width of the interval. For example, the integral of f(x)= 3 over the interval [0, 5] is 3 * 5 = 15.

Overall, the constant function is a simple but important concept in mathematics. Although it may seem trivial, it serves as a building block for more complex functions and is used in many practical applications, such as physics and engineering.

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