What do domain and range mean

You can also talk about the domain of a relation , where one element in the domain may get mapped to more than one element in the range. Here, the relation is given as a set of ordered pairs. Note that the domain elements 1 and 2 are associated with more than one range elements, so this is not a function.

But, more commonly, and especially when dealing with graphs on the coordinate plane, we are concerned with functions, where each element of the domain is associated with one element of the range. See The Vertical Line Test. The range is also all real numbers except zero. Domains can also be explicitly specified, if there are values for which the function could be defined, but which we don't want to consider for some reason. Let me ask you a question: Is square root a function?

If we say the codomain the possible outputs is the set of real numbers , then square root is not a function! A function must be single valued. It cannot give back 2 or more results for the same input. So, what we choose for the codomain can actually affect whether something is a function or not.

Mathematicians don't like writing lots of words when a few symbols will do. So there are ways of saying "the domain is", "the codomain is", etc. Dom f or Dom f meaning "the domain of the function f".

Ran f or Ran f meaning "the range of the function f". Hide Ads About Ads. Domain, Range and Codomain In its simplest form the domain is all the values that go into a function, and the range is all the values that come out.

However, we don't always have access to graphing software, and sketching a graph usually requires knowing about discontinuities and so on first anyway. In the numerator top of this fraction, we have a square root. In general, we determine the domain by looking for those values of the independent variable usually x which we are allowed to use.

We have to avoid 0 on the bottom of a fraction, or negative values under the square root sign. The range is found by finding the resulting y -values after we have substituted in the possible x -values. There would be a 0 on the bottom of the fraction. Range: No matter how large or small t becomes, f t will never be equal to zero.

There are no resulting square roots of negative numbers or divisions by zero involved here. The function is part of a parabola.

In case you missed it earlier, you can see more examples of domain and range in the section Inverse Trigonometric Functions. We fire a ball up in the air and find the height h , in metres, as a function of time t , in seconds, is given by.

Generally, negative values of time do not have any meaning. Also, we need to assume the projectile hits the ground and then stops - it does not go underground.

So we need to calculate when it is going to hit the ground. So we solve:. We can see from the function expression that it is a parabola with its vertex facing up. This makes sense if you think about throwing a ball upwards.

It goes up to a certain height and then falls back down. What is the maximum value of h? We use the formula for maximum or minimum of a quadratic function. By observing the function of h , we see that as t increases, h first increases to a maximum of Sometimes we don't have continuous functions. What do we do in this case? Let's look at an example. Disclaimer: IntMath. Problem Solver provided by Mathway. Bio: Hi! I am Ligia, I really enjoy mentoring others and have worked as a math tutor at Stanford.

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