. Construct a rational function whose only asymptotes are y=4 and x=1, and whose x intercept is (1/4,0) and y intercept is (0,1).

Answer 1

asymptotes y=4, x=1

x intercept is (1/4,0) y intercept (0,1)

y= 4x/(x-1) has the required asymptotes

to get the y intercept just add 1 but change 4 to 3 to keep y=4 as the asymptote

y = f(x) = 3x/(x-1) + 1 is the function you want

x intercept is when y=0

0 =3x/(x-1) +1

-1 = 3x/(x-1)

1-x = 3x

4x=1

x =1/4