Rational Functions of the Form

For this model, both the numerator and the denominator are linear expressions. We are getting close to maximum complexity…

Examine the following Vertical asymptote at x = 2. What about the horizontal asymptote?

As x approaches infinity,…. Both the numerator and denominator approach infinity, which can make it tricky to figure out… We will operate algebraically first…

Divide each term by x Now, as x approaches infinity, this term gets very close to zero

So, as

likewise, as

The function approaches the line y = 1 for both directions. So, y = 1 is the equation of the horizontal asymptote. (this makes the intercepts easier to find)

Intercepts? When x = 0, y = ? When y = 0, x = ?

At this stage, it may be easier to pick a few points near the asymptotes…

Examine the following model using the DIVER structure:

Sketch specifics: Domain Intercepts Vertical asymptote End Behaviour Range

Pg 174 1a,c,e 2a,c,e 3a,c,e DIVER on 3 10

End Behaviour as