SOLUTION: Sketch the graph of a function that has a horizontal asymptote of y=5, a vertical asymptote of x=2, an x intercept of -1, and a hole when x=1. Also, give one possible equation for

Algebra ->  Coordinate-system -> SOLUTION: Sketch the graph of a function that has a horizontal asymptote of y=5, a vertical asymptote of x=2, an x intercept of -1, and a hole when x=1. Also, give one possible equation for       Log On


   

Question 969314: Sketch the graph of a function that has a horizontal asymptote of y=5, a vertical asymptote of x=2, an x intercept of -1, and a hole when x=1. Also, give one possible equation for it.
I think I had this graph drawn correctly, but professor counted it incorrect. Not sure I had the correct equation though. Any help would be great...preparing for final exams.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=%28somethingofx%29%2F%28someotherofx%29

Root at -1, hole or undefined for x at 1:
f%28x%29=%28stillmoreofx%29%28%28x-1%29%2F%28%28x-1%29%29%28x%2B1%29%29

Vertical Asymptote x=2.
f%28x%29=%28stillmoreofx%29%28%28x-1%29%2F%28%28x-1%29%29%28x%2B1%29%28x-2%29%29
Notice the degree of the denominator is three, and degree of numerator is one, maybe higher but less than three. So far, the horizontal asymptote is 0; but you want it to be y=5.
... This is not yet finished, but maybe you see how to finish it.