Find a possible formula for the function graphed below Assum

Find a possible formula for the function graphed below Assume the function has only one x-intercept at the origin, and the point marked on the graph below is located at (6, 3/4) The asymptotes are x = -2 and x = 5 Give your formula as a reduced rational function.

Solution

asymptotes at x=-2, x=5

factors (x+2),(x-5) lies in the denominator

x intercept at origin

=>x-0 =x lie in numerator

general form of function that can be deduced from the given information is is y =ax_/(x+2)(x-5)

given (6,3/4) lies on the graph

(3_/4) =a*6_/(6+2)(6-5)

(3_/4) =a*6_/8

a=1

therefore the possible function is f(x) =x_/(x+2)(x-5)