SOLUTION: Sketch a 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 and give one possible equation for it.

Algebra ->  Functions -> SOLUTION: Sketch a 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 and give one possible equation for it.      Log On


   

Question 969596: Sketch a 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 and give one possible equation for it.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Horizontal Asymptote: Degree of numerator equals degree of denominator.

Vertical Asymptote x=2: something%2F%28x-2%29

x-intercept -1: %28something%28x%2B1%29%29%2F%28x-2%29

Hole and undefined at x=1: %28%28x%2B1%29%28x-1%29%29%2F%28%28x-2%29%28x-1%29%29

Almost finished. You want horizontal asymptote y=5. Leading terms must become increasingly large and positive as x goes to the right or left unbounded and ratio must approach 5.

highlight%28%285%28x%2B1%29%28x-1%29%29%2F%28%28x-2%29%28x-1%29%29%29
and you can multiply fully if desired.