constant function
A constant function is a type of function where the output (or value) is the same for every input
A constant function is a type of function where the output (or value) is the same for every input. In other words, it is a function that does not depend on the input value and always returns a fixed number.
The general form of a constant function is f(x) = c, where c is a constant value. This means that no matter what value of x you input into the function, the result will always be the same constant value.
Graphically, a constant function appears as a horizontal line on a coordinate plane. Since the y-value (output) remains constant regardless of the x-value (input), the line is parallel to the x-axis.
Some important properties of constant functions are:
1. Domain and range: The domain of a constant function is the set of all real numbers (since it can be evaluated for any value of x), and the range is a single value, which is the constant value itself.
2. Degree: A constant function has a degree of 0, as it does not involve any variables raised to a power.
3. Horizontal line test: Since a constant function is a straight horizontal line, it passes the horizontal line test. This means that the function is one-to-one and has an inverse function.
4. Differentiation: When differentiating a constant function, the derivative is always zero. This is because the function does not change with respect to the input.
For example, let’s consider the constant function f(x) = 5. No matter what value of x we plug into the function, the output will always be 5. The graph of this function is a horizontal line passing through the point (0, 5).
In summary, a constant function is a special type of function where the output is the same for every input. It has a degree of 0, a domain of all real numbers, and a range of a single value. The derivative of a constant function always evaluates to zero, and its graph is a horizontal line.
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