A function assigns the values. The function is f(x) = (8x - 8)/(x² + 2x).
A function assigns the value of each element of one set to the other specific element of another set.
A rational function has a denominator and a numerator.
Vertical asymptotes are x-values that the function approaches but never touches. By setting the denominator to zero, we may discover the vertical asymptotes.
Since the vertical asymptote is x=-2 and x=0, our denominator of the function will be
x(x+2) = x²+2x
Horizontal asymptotes are y values that the function approaches but never touches. Because the horizontal asymptote is y=0, the numerator's degree must be less than the denominator's degree. And because the x-intercept is equal to one, our numerator will be
x - 1
At the moment, The function can be assumed to be,
f(x) = (x - 1)/(x²+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.
The condition f(2)=1 must then be applied. If we substitute x=2, f(x) should equal 1. However, we must multiply the right side of the function by a constant C.
1 = C(2 - 1)/(2²+2(2))
Solve for C.
1 = C / 8
8 = C
So the function will be
f(x) = [8(x - 1)] / [(x² + 2x)]
f(x) = (8x - 8) / (x² + 2x)
Hence, the function is f(x) = (8x - 8)/(x² + 2x).
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