SOLUTION: Write an equation of a rational function {{{f(x)= p(x)/q(x)}}} having the indicated properties in which the degrees of p(x) and q(x) are as small as possible. More than one correc

Algebra ->  Graphs -> SOLUTION: Write an equation of a rational function {{{f(x)= p(x)/q(x)}}} having the indicated properties in which the degrees of p(x) and q(x) are as small as possible. More than one correc      Log On


   



Question 466847: Write an equation of a rational function f%28x%29=+p%28x%29%2Fq%28x%29
having the indicated properties in which the degrees of p(x) and q(x) are as small as possible. More than one correct function may be possible.
The function has to have a vertical asymptote of x=3, a horizontal asymptote of y=0, a y-intercept at -1, and no x-intercept.

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+3%2F%28x+-+3%29
There is vertical asymptote where x - 3 = 0, or x = 3.
When x--> infinity, y = f(x) --> infinity, so there is horizontal asymptote of y = 0.
When x = 0, f(0) = -1., and the graph doesn't intersect the x-axis, so there's no x-intercepts.