domain
That would be the domain.
The domain of the function means, for what values of the independent variable (input value) (or variables) is the function defined. If you have an equation of the type:y = f(x) ("y" somehow depends on "x") then the domain is all the values that "x" can take.
The range is a measure of the difference between the maximum and minimum values that a variable can take, or that a function can take over the relevant domain.
Find the maximum and minimum values that the function can take over all the values in the domain for the input. The range is the maximum minus the minimum.
domain
The domain of a function is the set of values for which the function is defined.The range is the set of possible results which you can get for the function.
That would be the domain.
The range of a function is the set of all of the possible values that it can take on as an output value. You find the range by inspecting the function and seeing first what the domain is, and then what the range would be for that domain. The domain, then, is the set of all of the possible values that it can take on as an input value.
The domain of the function means, for what values of the independent variable (input value) (or variables) is the function defined. If you have an equation of the type:y = f(x) ("y" somehow depends on "x") then the domain is all the values that "x" can take.
The range is a measure of the difference between the maximum and minimum values that a variable can take, or that a function can take over the relevant domain.
Find the maximum and minimum values that the function can take over all the values in the domain for the input. The range is the maximum minus the minimum.
The domain is the set of values that x may take that gives back an answer that makes sense. The range is the set of values that are possible results of the function. the "log" function does not accept 0 or negative values on its domain and returns negative, zero and positive numbers (ie all real values). The next function does not appear properly but you could figure it out
The function ( f(x) = 4x ) is a linear function. Its domain includes all real numbers, as there are no restrictions on the values that ( x ) can take. Therefore, the domain of ( f(x) ) is ( (-\infty, \infty) ).
Yes. A function is a rule to assign a value based on some other value; you can make the function equal to a constant for all values of a variable "x", or you can make it equal to a few values. Commonly used functions of this type include the integer function (take the integer part of a number), which, if you consider a finite domain (for example, all numbers from 0 to 10), has an infinite number of values in the domain, but only a few specific values in its range; and the sign function.
When the variables take fractional values, particularly if the domain and codomain are not very big.When the variables take fractional values, particularly if the domain and codomain are not very big.When the variables take fractional values, particularly if the domain and codomain are not very big.When the variables take fractional values, particularly if the domain and codomain are not very big.
By having some knowledge about the functions involved. The natural domain is the domain for which the function is defined. For example (assuming you want to work with real numbers): The square root of x is only defined for values of x greater or equal to zero. The corresponding range can also be zero or more. The sine function is defined for all real numbers. The values the function can take (the range), however, are only values between -1 and 1. A rational function (a polynomial divided by another polynomial) is defined for all values, except those where the denominator is zero. Determining the range is a bit more complicated here.