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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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Q: How do you determine the domain and range of relations and functions?

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The same as in any other math class. All functions are relations but all relations are not functions. A function must have only one 'answer' in the range for each value of the domain. Relations are just pairing of numbers with no such restriction on the range.

No domain no range

All functions are relations with the condition that each element of the domain is paired with only one element of the range. A relation is any pairing of numbers from the domain to the range.

true

True.

A number does not have a range and domain, a function does.

The domain and range of the composite function depend on both of the functions that make it up.

true

Domain and range are used when you deal with functions - so basically you use them whenever you deal with functions.

You do not graph range and domain: you can determine the range and domain of a graph. The domain is the set of all the x-values and the range is is the set of all the y-values that are used in the graph.

true

i think that the range and the domain of a parabola is the coordinates of the vertex

It can be quite hard. First determine the domain. Then, for every input value from the domain, calculate the output value. The set of all these output values is the range. For simple functions you will not need to find every output value. For monotonic continuous functions the end points of the domain will determine the endpoints of the range. [Monotonic means never decreasing or never increasing]. For non-monotonic functions, for example a quadratic or polynomial of higher order, you may need to find the turning points.

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.

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 inverse of the inverse is the original function, so that the product of the two functions is equivalent to the identity function on the appropriate domain. The domain of a function is the range of the inverse function. The range of a function is the domain of the inverse function.

The domain of x^3 - 2x is whatever you choose it to be. That will then determine the range.

Domain and range are not sufficient to determine the y intercept. For example, the domain and range for the straight line y = 2x + 3 are the whole of the real numbers. That tells you nothing about the intercept.

The domain is the set of the first number of each ordered pair and the range is the set of the second number.

Yes, for some functions A, and not for others.

let f ={(x,xsquare/1+xsquare)} be a function from R in to R. Determine the range f.

You can define the domain as anything you like and that will determine the range. Or, you can define the range as anything you like and that will determine the domain. For example: domain = {1, 2, 3, 4, ... } then range = {-3, 0, 5, 12, ... } or range = {1, 2, 3, 4, ... } then domain = {sqrt(5), sqrt(6), sqrt(7), sqrt(8), ...}. There is, of course, no need to restrict either set to integers but then it was easier to work out one set from the other.

Domain is what you can plug into the function (possible x values for y=f(x) type functions) and range is the possible values you can get out (possible y values).

The domain and range are two different sets associated with a relationship or function. There is not a domain of a range.

range

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