Constant function
f(x) = b
A constant function is a type of mathematical function that always produces the same output for every input. In other words, it is an algebraic expression that remains unchanged no matter the value of the independent variable. For instance, the function f(x) = 3 is a constant function because it always equals 3 for any value of x.
The graph of a constant function is a straight line parallel to the x-axis, passing through the y-value of the constant term. Since the function produces the same output for every input, the graph remains a horizontal line, irrespective of the x-value.
The derivative of a constant function is always zero, which means that it has no slope or rate of change. The integral of a constant function is the product of the constant term and the variable.
In practical applications, constant functions are commonly used to represent fixed costs, such as rent or taxes, that do not vary with production levels. They are also useful in trigonometry, where they are used to model certain cyclic phenomena, such as the position of celestial bodies.
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