How to Find the Domain & Range of a Function

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Finding the domain and range of a function is as simple as finding the possible X and Y values, respectively. Learn about X and Y values as dependent and independent variables with help from a math teacher in this free video on math functions and lessons.

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Video Transcript

So, how does one find the domain and range for a function? Hi. I'm Jimmy Chang and I've been teaching college mathematics for nine years. And, in order to find the domain and range of a function, it's really important that you understand the definitions behind the two first. So, here's an overview as to what domain and range are all about. Now, the domain. Rough definition, it would be the set of possible X values. In other words, what numbers are you allowed to plug in for X? Now, in the range is a set of possible Y values. In other words, what are the numbers that are possible for Y? Now, oftentimes, you might have heard that X is the independent variable and Y is the dependent variable. In other words, what numbers the Y can be really depends on what numbers the X is going to be. So, in other words, when you plug in the X values, you'll get your Y values. So, domain is what's allowed for X and range is what's allowed for Y. So, here's a couple of quick examples for you. Now, suppose you have a function, Y= 3x 1. Now, first you generally want to find the domain. Now, in terms of domain, you want to figure out what's allowed for X. Now, basically, because it's 3x 1, you might recognize this as a line. Now, you can figure out down the line that any number is possible to plug in for X. So, basically, a short answer for domain is all real numbers. Or, if you're familiar with integral notation, you will say negative infinity to positive infinity. Now, what about the range? What is allowed for Y? Well, if you can plug in any number you want for X, then you can plug in any number you want for Y. So, therefore, the range is also all real numbers. Now, suppose you have something of the sort of Y equals the square root of x. Now, in this particular case, you have a square root function. Now, square root functions, you know, has to be positive or zero. So that means for the domain, you can plug in only numbers bigger than or equal to zero, because again, square roots, you can't really have negative numbers, otherwise you'll have imaginary, which you can't really have for real numbers. So, the domain is all numbers X greater than or equal to zero. Now, if you can only plug in positive numbers or zero for X, then that means the Y ones are also going to be positive or zero. So that means your range, in this particular case, is also going to be greater than or equal to zero. Now, aren't the domain and range always going to match? No, not necessarily. It all depends on the function. But, I'm Jimmy Chang and that gives you a glimpse as to how you find domain and range.


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