Learn math, science, English SAT & ACT from
highquaility study
videos by expert teachers
Thank you for watching the preview.
To unlock all 5,300 videos, start your free trial.
Graphing a Rational Expression  Problem 1
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
Graphing a simple rational expression with a transformation so for this example we are going to look at f(x) is equal to one 1 over x plus 2. And what I want to do is draw some parallels to some other functions that we are doing now.
So say we are talking about f(x) is equal to x². We know that graph to be a basic parabola and if I said g(x) is equal to x² minus 4 that’s going to shift the graph down 4. So basically it’s going to keep the same shape and instead of going through the origin, it’s now going to go down 4 units and look pretty much the same. Just a rough sketch of what’s going on with this.
With rational expressions the idea is exactly the same. We know what 1 over x looks like, we know that 1 over x looks like this so all we do with the plus 2 is it shifts everything up 2 spaces. So the graph of this gets moved up 2. We have vertical asymptote at the y axis if we move our vertical line up and down it stays the same. But what is going to change is we have a horizontal, normally we have a horizontal asymptote at 0. That gets moved up 2 so what actually happens is we know how our horizontal axis asymptote right there. I always draw it in just to sort of keep my point of reference on what’s going on, and then our graph is going to keep the exact same shape.
Something like this something like that so basically all we’ve done is we’ve taken our normal 1 over x graph and just moved it up two units vertical asymptote stays the same, horizontal asymptote gets moved up 2, so horizontal asymptote is now at y equals 2.
Please enter your name.
Are you sure you want to delete this comment?
Carl Horowitz
B.S. in Mathematics University of Michigan
He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his stepbystep explanations are easy to follow.
Concept (1)
Sample Problems (12)
Need help with a problem?
Watch expert teachers solve similar problems.

Graphing a Rational Expression
Problem 1 4,713 viewsGraph:
f(x) = 1 + 2 x 
Graphing a Rational Expression
Problem 2 4,175 viewsGraph:
f(x) = 1 x + 3 
Graphing a Rational Expression
Problem 3 4,026 viewsGraph:
f(x) = 1 x 
Graphing a Rational Expression
Problem 4 1,257 views 
Graphing a Rational Expression
Problem 5 993 views 
Graphing a Rational Expression
Problem 6 986 views 
Graphing a Rational Expression
Problem 7 1,105 views 
Graphing a Rational Expression
Problem 8 1,022 views 
Graphing a Rational Expression
Problem 9 942 views 
Graphing a Rational Expression
Problem 10 961 views 
Graphing a Rational Expression
Problem 11 991 views 
Graphing a Rational Expression
Problem 12 967 views
Comments (0)
Please Sign in or Sign up to add your comment.
·
Delete