####

#### To continue with our investigation, let's look at
the quotients of f(x) and g(x) where

#### f(x) = -3

#### g(x) = 5

#### h(x) = -3/5

####

#### Again we start off with straight lines.

####

#### What happens when we make n=6

#### f(x) = 6x - 3

#### g(x) = 6x + 5

#### h(x) = (6x - 3)/(6x + 5)

####

#### It appears that we have a hyperbola
instead of a straight line.

####

#### Let's check this out with n
= 20 to see if it is a trend

#### f(x) = 20x - 3

#### g(x) = 20x + 5

#### h(x) = (20x - 3)/(20x + 5)

####

#### Not only do we get another
hyperbola, but it looks like in both cases where we had a hyperbola
that h(x) also has an asymptote

#### From what we know about functions,
we know that h(x) is discontinuous when its denominator is equal
to zero.

#### Therefore in the last case
h(x) is discontinuous when:

#### 20x + 5 = 0

#### 20x = -5

#### x = -5/20

#### x = -1/4

#### To see if there will always
be discontinuity let's look at the general case

#### f(x) = ax + b

#### g(x) = cx + d

#### h(x) = (ax + b)/(cx + d)

#### therefore the function would
be discontinuous when:

#### cx + d = 0

#### cx = -d

#### x = -d/c

#### Therefore, if f(x) and g(x)
are linear functions their quotient, h(x), will always have an
asymptote located at x = -d/c

####