SOLUTION: A function f has a horizontal asymptote of y = -4, a vertical asymptote of x = 3, and an x-intercept at (1,0). Part (a): Let f be of the form f(x) = (ax+b)/(x+c). Find an expres

Question 1092988: A function f has a horizontal asymptote of y = -4, a vertical asymptote of x = 3, and an x-intercept at (1,0).
Part (a): Let f be of the form f(x) = (ax+b)/(x+c). Find an expression for f(x).
Part (b): Let f be of the form f(x) = (rx+s)/(2x+t). Find an expression for f(x).
Answer by greenestamps(13209) (Show Source): You can put this solution on YOUR website!

Part (a): Let f be of the form

The horizontal asymptote is the ratio of the coefficients of the x term in the numerator and denominator.

So a = -4.

The vertical asymptote is where the denominator is 0: at x = 3.

So c = -3.

f(1) = 0:

So b = 4.

The completed rational function is

Part (b): Let f be of the form

The horizontal asymptote is the ratio of the coefficients of the x term in the numerator and denominator.

So r = -8.

The vertical asymptote is where the denominator is 0: at x = 3.

So t = -6.

f(1) = 0:

So b = 8.

The completed rational function is

Note that is in the form required for part (b). However, in simplified form the function is

which is the same function as in part (a).

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