Question

6d) write an equation in the form r(x) = p(x) / q(x) for each function shown below.Note: The data can be obtained from the graph in picture

Answer 1

F(x) =a (x-b) /(x-c )(x-d)

Vertical asymptote : x =1; therefore c = 1

therefore F(x) = a(x-b)/(x-1)

2. horizontal asymptote y = -3

x -intercept at (1/2; 0) , so b = 1/2 , then F(x) = a(x-1/2) ( x-1)

the graph passes through (0;-1) , so finding a :

-1 = a(0-1/2)/ (0-1) ';

-1(-1) = -1/2 a therefore a = -2* (1) ; so a = -2

so the graph will be y = -2 ((x-1/2) / (x-1)