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Introduction to Rational Functions - Concept
We have rational functions whenever we have a fraction that has a polynomial in the numerator and/or in the denominator. An excluded value in the function is any value of the variable that would make the denominator equal to zero. To find the domain, list all the values of the variable that, when substituted, would result in a zero in the denominator.
A rational function is a fraction that has polynomials in the numerator and denominator. Now remember that a numerator is the top and denominator is the bottom and a polynomial might take on the form of a monomial which is just one term like 3 or 3x or it might be something scarier like a 4 term polynomial that has lots of exponents and letters involved. So we're dealing with big old nasty fractions, pretty much. Rational functions means big old nasty fraction.
When you're working rational fractions, rational functions, it's important that you guys are aware of what we call excluded values. Excluded value is any value of the variable that would make the denominator equal to zero. And the reason why you guys know about fractions, you can have whatever you want you're going on in the numerator, but in the bottom thou shall not divide by zero. That's an important Math rule that continues throughout your entire math career. An excluded value would be anything that would make this numerator or this denominator equal to zero. Or would make the function undefined.
Later on you'll start seeing how this connects to asymptotes on the graph. That will come in later in your Math career but for now it's important for you guys just to know that an excluded value of a rational function is any value of x or the variable that would make the denominator equal to zero or undefined. It will make more sense once you start practicing working with those rational function fractions.