A constant function is where the output variable (e.g. y) is not dependent on the input variable (e.g. x). Generally, it is a function which always has the same value no matter what the input is.
We can write this type of function as:
f(x) = c
- c is a constant: a number that doesn’t change as x changes.
For example, the following are all constant functions:
- f(x) = 99,
- f(x) = .1 and
- f(x)= -21
Since f(x) is equal to a constant, the value of f(x) will always be the same no matter what the value of x might be.
The Graph of a Constant Function
In a two dimensional plane, the graph of this type of function is a straight, horizontal line. It passes through the point (0, c), (1, c), and (-1, c). In fact, (a, c) for any a on the number line.
For example, the graph of the constant function f(x) = 4 is a straight, horizontal line that passes through the points (2,4), (0,4), and (-2,4). This graph is shown below.
Every function with a derivative equal to zero is a constant function.
The integral of this type of function is equal to c x. For example, the integral of f(x) = 10 is 10x.
The following shows the graph of f(x) = 10, and the integral f(x) = 10x. The blue square represents the integral when evaluated from 0 to 1.
Limit of a Constant Function
Applications of the Constant Function
Though it is one of the simplest type of functions, it can be used to model situations where a certain parameter is constant and isn’t dependent on the independent parameter. For instance, a school dining room where every child was given one donut, irrespective of age, or an exam in which every student was given an A regardless of how hard they worked.
Maplesoft Support. Online Help: Math Apps: Functions and Relations.Retrieved from https://www.maplesoft.com/support/help/Maple/view.aspx?path=MathApps%2FConstantFunction on May 24, 2019.
Stephanie Glen. "Constant Function: Simple Definition & Example" From CalculusHowTo.com: Calculus for the rest of us! https://www.calculushowto.com/constant-function/
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