How to Find Domain and Range

Domain and Range

State the domain and range of the function y equals x squared plus 5. In order to do this, we first need to understand what a domain and a range is. The domain of a function is all the possible values that could be plugged in for x, any number that could be plugged in for x. The domain is the set of all permissible inputs. Inputs again being x values, the numbers that can be plugged in for x. Any number that can be plugged in for x, and the domain is the whole set of those numbers.

The range then is once those numbers are plugged in, what are the values for y? Because the range is the whole set of y values. It’s the set of all possible outputs. (Output being y value.) Now that we understand what these words mean we can answer this question. The domain again is the set of all permissible inputs, so basically which numbers can be plugged in for x. Looking at our function, what numbers could we plug in for x? Really, any real number positive, negative, a square root number, anything we wanted to plug in would work in this function. Our domain then is all real numbers.

Now for the range, again the range is the set of all the possible outputs or y values once we’ve plugged in our domain or our set of inputs. Since our x is squared, that means that our answer is always going to be a positive number, we can never get a negative number since we’re squaring x. Even negative 4 squared would be a positive 16. The lowest this square could possibly be would be zero, because zero squared would give you zero. Then with this plus 5 that now means that the lowest value that y will ever be is a positive 5.

Your range would be all real numbers greater than or equal to 5, since 5 is the lowest it can go. 5 would be the lowest value, but then of course it could be anything above 5. There’s the domain and the range.