Michael J. answered • 08/31/15

Effective High School STEM Tutor & CUNY Math Peer Leader

A rational function is one that has a numerator and a denominator.

Vertical asymptotes are values of x in which the function gets closer to, but never touches. We can find the vertical asymptotes by setting the denominator equal to zero.

Since the vertical asymptote is x=-2 and x=0, our denominator of the function will be

x(x + 2) = x

^{2}+ 2xHorizontal asymptotes are values of y in which the function gets closer to, but never touches. Since the horizontal asymptote is y=0 , the degree of the numerator must be less than the degree of the denominator. And since the x-intercept is x=1, our numerator will be

x - 1

So far, we can assume the function to be

f(x) = (x - 1) / (x

^{2}+ 2x)Next, we need to use the condition f(2)=1. If we plug in x=2, f(x) should equal 1. But we need to multiply the right side of the function by some constant C.

1 = C(2 - 1) / (2

^{2}+ 2(2))Solve for C.

1 = C / 8

8 = C

So the function will be

f(x) =

**[**8(x - 1)**]**/**[**(x^{2}+ 2x)**]**f(x) = (8x - 8) / (x

^{2}+ 2x)