Learn math, science, English SAT & ACT from
highquaility study
videos by expert teachers
Learn math, science, English SAT & ACT from
highquaility study videos by expert teachers
Introduction to Rational Functions  Problem 3
Alissa Fong
Alissa Fong
MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
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. Ohoh! 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.
Please enter your name.
Are you sure you want to delete this comment?
Alissa Fong
M.A. in Secondary Mathematics, Stanford University
B.S., Stanford University
Alissa has a quirky sense of humor and a relatable personality that make it easy for students to pay attention and understand the material. She has all the math tips and tricks students are looking for.
Concept (1)
Sample Problems (8)
Need help with a problem?
Watch expert teachers solve similar problems.

Introduction to Rational Functions
Problem 1 5,143 viewsFind the domain of
f(x) = 4 x 
Introduction to Rational Functions
Problem 2 4,105 viewsFind the domain of
f(x) = 4 x − 3 
Introduction to Rational Functions
Problem 3 3,635 viewsFind the domain of
f(x) = 4 2x² + 5x + 3 
Introduction to Rational Functions
Problem 4 749 views 
Introduction to Rational Functions
Problem 5 583 views 
Introduction to Rational Functions
Problem 6 666 views 
Introduction to Rational Functions
Problem 7 612 views 
Introduction to Rational Functions
Problem 8 569 views
Comments (0)
Please Sign in or Sign up to add your comment.
·
Delete