Need help with the following:
Find a rational function that has x=2 and x=-1 as vertical
asymptotes, and (4,0) as an x-intercept.
A rational function is a fraction, so we write y = a fraction bar:
y = 覧覧覧覧覧覧覧覧
To have a vertical asymptote of x = 2 we must have gotten that equation by
setting one of the factors of the denominator = 0 and solving for x.
To have gotten x = 2, we must have set x - 2 = 0. Therefore (x - 2)
must be a factor of the denominator. So we now have
y = 覧覧覧覧覧覧覧覧
(x - 2)
To have a vertical asymptote of x = -1 we must have gotten that equation by
setting one of the factors of the denominator = 0 and solving for x.
To have gotten x = -1, we must have set x + 1 = 0. Therefore (x + 1)
must be a factor of the denominator. So we now have
y = 覧覧覧覧覧覧覧覧
(x - 2)(x + 1)
To have (4,0) as an x-intercept, y must be 0 when x = 4. So the numerator
could have as a factor x - 4, since that is 0 when x = 4. So the easiest
answer is
x - 4
y = 覧覧覧覧覧覧覧覧
(x - 2)(x + 1)
or you can multiply the bottom out if you like and get
x - 4
y = 覧覧覧覧覧覧
xｲ - x - 2
Edwin McCravy
AnlytcPhil@aol.com