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Introduction to Rational Functions - Problem 3
In order to find the domain of a rational function, I first of all look out for excluded values. Excluded values are any x value that would make the denominator equal to 0.
So in my case I’m going to solve the equation 2x² plus 5x plus 3 equals 0. That’s going to help me find my exclude values. So I could use the quadratic equation or I can complete the square or I can use factoring that’s what I’m going to choose, graph it. You guys know all the different kinds of methods for solving quadratic equation. Personally I like factoring.
Okay so I know my first two values have to have a product of two, my last two numbers have to have a product of 3, so I’m going to try using 3 and 1 Foiling my head. Oh-oh! That’s not right because that would give me 7X's that’s not right I’m going to make that 1 and 3. Guess and check is the bummer of factoring.
Now let's try to foil 2x² good, plus 2x it's really good, so now I have this 5x plus 3, that’s the correct factorization. So to continue solving I’m going to use the zero product property. I’m going to set each one of these factors equal to 0 and then solve for x. X is going to be equal to -1 that’s one of my excluded values and also I’m going to have x is going to be equal to -3/2. Those are my two excluded values. Don’t get confused I’m not looking for these x answers, these are the things that would make my function undefined.
I want the domain so here it comes. The domain means the set of possible x numbers that I could input into this function. It’s going to be all real numbers any value I want to, except my excluded values. Except -3/2 and -1 that’s my domain. If I were to make a table to graph this or if I were to graph this and look for asymptotes, I’d be looking for any x number that’s not equal to -3/2 and not equal to -1.
Again these are the excluded values those are the domain. Those are the things that are excluded from the domain it;s really tricky. Be careful because these are the guys that make the function undefined.