+0  
 
+1
54
1
avatar+18 

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)

 Jul 30, 2020
edited by unknowledgeable  Jul 30, 2020
 #1
avatar+21953 
0

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.

 Jul 30, 2020

16 Online Users

avatar
avatar