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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.
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Domain and range of a function?
The domain of a function determines what values of x you can plug into it whereas the range of a function determines the values that are your results. Therefore, look at the y-axis if you want to determine the range of a function and look at the x-axis if you want to determine the domain.
How do you find the range with the domain?
Find the range of a function by substituting the highest domain possible and the lowest domain possible into the function. There, you will find the highest and lowest range. Then, you should check all the possible cases in the function where a number could be divided by 0 or a negative number could be square rooted. Remove these numbers from the range. A good way to check to see if you have the correct range is to graph the function (within the domain, of course).
The number 5 is in both the domain and the range of the function A?
true
What best describes the domain of a function?
The range of a function is the set of all possible input values.
What is the range of the function y equals x2 plus 1?
The answer depends on the domain. If the domain is the whole of the real numbers, the range in y ≥ 1. However, you can choose to have the domain as [1, 2] in which case the range will be [2, 5]. If you choose another domain you will get another range.
