How to Find the Range of a Function in Math

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The range of a function in math refers to all of the Y values that the function covers, while the domain refers to the X values that a function covers. Find the range of a function with information from a standardized test prep instructor in this free video on education.

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Let's talk about how to find the range of a function in math. So range is a specific vocabulary word. These are kind of cool because if you don't know the word, you can't really get it. If you do know the word, it's really not that bad. So once you get past the intimidation or the not knowing, it's really not that big of a deal. Range is just a very specific math vocabulary word meaning what Y values does the function cover, and I'll show you what I mean in a minute. And just so you know, the other one is domain. Domain is a fancy word for what X values does the function cover? So let's take a look at two functions. Here's a simple linear function. Linear is just a vocabulary word for line -- it's the function of a line. Now, a line -- just a normal old line -- which is usually, like, Y equals MX plus B. A normal line, the range is all real numbers. All numbers are covered. This line will eventually -- that's why we have arrows -- will eventually cover all Y values up into infinity, and then down below. It'll go...it'll cover... Every Y value will eventually have a point on this line. So the range of this line is all real numbers. That's a symbol for all real numbers. Or you can just write all reals -- whatever your math teacher uses. Now, here's an example of another function. This function is quadratic -- it's the other kind you use in Algebra I or Algebra II. Linear function means a line. Quadratic function means that it's this U-shaped graph -- a parabola is the other word for it. Now, these...what you've got to say is what Y values are covered here? Incidentally, the domain -- the X values -- we're going to cover all X values here, even though it looks like it slopes down, it's actually going that way. So eventually, all X values and all X values this way and that way will be covered. But Y values, the range, we're only actually going to get Y values less than or equal to zero because here's the zero line for Y, and we only have values for Y that are lower than that. You're never going to have a Y value in this graph that is greater than zero. So the range of this function is Y is less than or equal to zero.

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