Introduction to Rational Functions - Problem 2


I’m going to look at this function and try to find the domain. Remember the domain is the set of all possible input or x values. In order to find the domain I’m going to think about what we call the excluded value. An excluded value would be any value of x that would make this function undefined. A function is undefined if the denominator or the bottom is equal to 0.

So my excluded value is going to be the value x equals 3. That’s an excluded value because if x were a 3 this denominator would be 0 and that’s bad news. So when you ask me to find the domain I would say x is all real numbers except for 3. x is all reals, I guess I’m just going to say the domain is all real numbers, you can abbreviate that with ‘all reals' except 3, because 3 is what we call an the excluded value. When you guys start making the graphs of these you'll see when it shows up in an asymptote. For now it’s advised to say the domain is any value, any real number except for 3 because if x were equal to 3, that fraction would be undefined.

rational function excluded value domain asymptote