The union symbol is used when we have a function whose domain or range cannot be described with just a single interval. The range can therefore be written in interval notation as: Recall that the range of f(x) = x 2 is all positive y-values, including 0. We used parentheses rather than brackets around each endpoint because the endpoints are negative and positive infinity, which by definition have no bound. In other words, any value from negative infinity to positive infinity will yield a real result. Recall that the domain of f(x) = x 2 is all real numbers. Let's look at the same example as above, f(x) = x 2 to see how interval notation is used. The endpoints are written between either parentheses or brackets, depending on whether the endpoint is included or not.The first term is the left endpoint and the second term is the right endpoint.The smallest term in the interval is written first, followed by a comma, and then the largest term.When indicating the domain in interval notation, we need to keep the following in mind: The table below shows the basic symbols used in interval notation and what they mean: When using interval notation, domain and range are written as intervals of values. Two of these notations are interval notation and set notation. This makes it far easier to express the domains and ranges of multiple functions at a time, particularly as functions get more complicated. While this is possible for all functions, different notations have been developed for expressing domains and ranges in a more concise way. Notice in the examples above that we described the domain and range using words. Thus, the range of f(x) = x 2 is all positive y-values.

Then, from looking at the graph or testing a few x-values, we can see that any x-value we plug in will result in a positive y-value. Thus, the domain of f(x) = x 2 is all x-values. Now try different functions from the 'Choose function' pull-down menu at the top of the domain and range calculator.There are no x-values that will result in the function being undefined and matter what real x-value we plug in, the result will always be a real y-value.The range arrow is solid when the range has fixed upper and lower bounds, but is dashed when the range goes off to infnity in either direction.Observe the resulting range, indicated by the height of the green rectangle, and of the pink arrow (which is solid if the range has defined limits, and dashed if the range goes off to infinity in either direction).Use the slider below the curve to change the domain of the function.In this calculator, you start with a predefined function that has been drawn for you. NOTE: We are dealing with real numbers only in this work.

$visual domain and range calculator$

In this interactive calculator, you can change the domain and see the effect on the range of several different trigonometric functions. Additionally, when calculating the domain be aware that the denominator of a fraction cannot be zero and the number under square root must be positive for the function to be correctly calculated. This calculator lets you explore the domain and range examples discussed on the previous page, Domain and Range of a Function.Īs a quick refresher, recall that the domain is the set of all possible x-values which will make the function 'work', and will output real y-values.

Visual domain and range calculator