Find a possible formula for the function graphed below. The x-intercept is marked with a point located at (5,0), and the y-intercept is marked with a point located at (0,−0.833333333333333). The asymptotes are y=−1 and x=6. Give your formula as a reduced rational function.

Answer 1

vertical asymptote at x=6
and a horizontal asymptote means
y = a(x-b)/(x-6) + c

y(5) = 0, so b=5

y = a(x-5)/(x-6) + c

y(0) = -5/6 and
y(∞) = -1, so
5/6 a + c = -5/6
a + c = -1

1/6 a = -1/6
a = -1
c = 0

y = (5-x)/(x-6)