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Graphing a Rational Expression - Problem 2

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

Dealing with the basic rational expression graph and some basic transformations. So for this example what I want to look at is 1 over x plus 3 and before I do that I want to take a look at our basic graph for 1 over x.

So we know the basic shape of 1 over x and we know that we have a horizontal asymptote at 0 and a vertical asymptote at 0 as well. So the reason we have a vertical asymptote at 0 is because we cannot plug 0 into this equation.

When we plug numbers in very close to 0 it's either they are going to go up to infinity or down to negative infinity. We plug in 1 over 100 1 over 100 turns into 100 so we get really close to our y axis we have a huge number.

So that’s why we have this vertical asymptote at 0. Going back over to this problem here what number can we not plug? We can’t plug in -3. So for this case what actually is happening to our problem is our graph is getting moved backwards three units.

We can’t plug in -3 so our vertical asymptote is now at -3. We’ve moved everything back you move a horizontal line backwards it stays in the same place, so what we really end up with is a graph that has the same shape as before everything moved back three, giving us a shape something like that. If this was a x minus we would’ve moved forward same idea what value of x can we not put in that’s where our vertical asymptote is going to be.

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