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In mathematics, a constant function is a function whose values do not vary and thus are constant. For example, if we have the function f(x) = 4, then f is constant since f maps any value to 4. More formally, a function f : Aâ†’ B is a constant function if f(x) = f(y) for all x and y in A.
Every empty function is constant, vacuously, since there are no x and y in A for which f(x) and f(y) are different when A is the empty set. Some find it more convenient, however, to define constant function so as to exclude empty functions.
In the context of polynomial functions, a non-zero constant function is called a polynomial of degree zero.
Constant functions can be characterized with respect to function composition in two ways.
The following are equivalent:
- f : Aâ†’ B is a constant function.
- For all functions g, h : Câ†’ A, fog = foh, (where "o" denotes function composition).
- The composition of f with any other function is also a constant function.
In contexts where it is defined, the derivative of a function measures how that function varies with respect to the variation of some argument. It follows that, since a constant function does not vary, its derivative, where defined, will be zero. Thus for example:
- If f is a real-valued function of a real variable, defined on some interval, then f is constant if and only if the derivative of f is everywhere zero.
For functions between preordered sets, constant functions are both order-preserving and order-reversing; conversely, if f is both order-preserving and order-reversing, and if the domain of f is a lattice, then f must be constant.
Other properties of constant functions include:
- Every constant function whose domain and codomain are the same is idempotent.
- Every constant function between topological spaces is continuous.
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Answers:I concur. "Controlled variables are quantities that a scientist wants to remain constant" "Some people refer to controlled variables as 'constant variables.' " Tell your teacher to change your text book ;p
Answers:The independant is the one you control directly and vary. Changes in the dependant result from this. (if you were plotting on a graph, you plot the independant on the x axis and the dependant on the y) A variable held constant is one that you can vary but choose not to. If you have a problem with multiple independant variables and you wish to investigate just 1 you would hold the others constant (eg if you were investigating how the rate of photosynthesis in a plant varied you might vary light levels while holding levels of water and carbon dioxide constant)
Answers:A controlled variable could change, but it will change the same for all treatments. For instance, if you add different amounts of water to plants (independent variable) and measure growth (dependent variable) and you grow them in a greenhouse, the amount of light will be a controlled variable (the light will vary and it will affect plant growth, but it will affect the independent and dependent variable the same). This way you can attribute changes you observe to the independent variable. I hope that makes some sense.
Answers:In All experiments the control is a variable that you the student scientist are able to change with different trails for instance you can vary the amount of sunlight a plant will get on a daily basis. one day it can get 5hrs, the next 2 hrs. The constant in any experiment is a variable that you are not able to change for instance if you are useing chemicals or if you are given a certain tyoe f plant that must remain constant and you are not able to change it. but you make the decision which variables in an experiment will be constant and what will be the control.