+19 A function f has a horizontal asymptote of y=-4, a veritcal asymptote of x=3, and an x-intercept at (1,0).
Part (a): Let f be of the form
\(f(x) = \frac{ax+b}{x+c}\)
Find an expression for f(x)
Part (b): Let f be of the form
\(f(x) = \frac{rx+s}{2x+t}\)
Find an expression for f(x)
+23246 Since there is a vertical asymptote of x = 3, there will be a factor of (x - 3) in the denominator.
This makes c = -3.
Since there is a horizontal asymptote of y = - 4, the ratio ax/x must be -4.
This makes a = -4.
Since there is an x-intercept at (1,0), we can look at y = (-4x + b) / (x - 3)
and substitute 1 for x and 0 for y: 0 = (-4·1 + b) / (0 - 3).
This makes b = 4.
f(x) = (-4x + 4) / (x - 3)
To get the answer to b, multiply both the numerator and denominator by 2.
