Question

State the equation of a rational function in the form f(x)=(ax+b)/(cx+d), if the vertical asymptote is x=3/5, the horizontal asymptote is y=4/3 and the y-intercept is (0,2). Make sure the numerator and denominator include only integers

Answer 1

vertical asymptote is x=3/5, so cx+d = 5x-3
horizontal asymptote is y=4/3, so a/c = 4/3, making a = 20/3
Now we have
y = (20/3 x + b)/(5x-3) and y(0) = 2, so
b/-3 = 2, making b = -6
y = (20/3 x - 6)/(5x-3) = (20x-18)/(15x-9)

Answer 2

Thank you!