Some functions are only defined for certain values of the argument. For example, the the logarithm is defined for positive values. The inverse function is defined for all non-zero numbers.
Sometimes the range determines the domain. If you are restricted to the real numbers, then the domain of the square root function must be the non-negative real numbers.
In this way, there are definitional domains and ranges. You can then chose any subset of the definitional domain to be your domain, and the images of all the values in the domain will be the range.
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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.
The domain is the set of all input values, the range is the set of all output values. It is not possible to be more specific when you have not included any details of the functions.
y = 1/x
sqrt(x) Domain: {0,infinity) Range: {0,infinity) *note: the domain and range include the point zero.
x = the domain y = the co-domain and range is the output or something e_e