Can a non-function equation still have a domain and range? - Answers

Yes. An equation that is not a function is called a relation. Functions are special types of relations where every input (or in other words each value in the domain) has exactly one output (or matches up with exactly one value in the range). A relation would be where you plug in a number for x but instead of only getting one number out for y, you get more than one. Example: y2=x If you plug in 4 for x and solve for y by taking the square root, then y could equal either positive 2 or negative 2, since 22 is 4 and (-2)2 is also 4. In this case, x corresponds with two output values for y (2 and -2) which means that while this equation is a relation, it is not a function. Domain here would refer to all numbers that make sense for x. In other words, what numbers can you plug in for x, and get an answer that is not imaginary or undefined. In the example above, I could not plug in negative numbers for x, because when I try to solve for y I would get an imaginary number. So we would say that the domain of that relation is x> or equal to 0. The Range for a relation is all of the possible output values. So for all the values of x that you can plug in, what are all the possible values of y I could get out? If you look at it, since I'm only plugging in 0 for x or any other number larger than 0, that would imply that y can only be 0 or bigger as well. So the range here would be y > or equal to 0. I hope that helps!