Find a rational function fx that satisfies the given conditi

Find a rational function, f(x), that satisfies the given conditions. There is no unique answer. vertical asymptotes: x = 3, x = 3 horizontal asymptote: y = 5 xintercept: (5, 0)

Solution

vertical asymptotes: x = 3, x = 3

=>factors of denominator are (x+3),(x-3)

horizontal asymptote: y = 5

=>leading coefficient is 5, heighest degree of numerator is 2

so function is of the form y=(5x²+c)_{/((x+3)(x-3))}

xintercept: (5, 0)

=>(5*5²+c)_{/((5+3)(5-3))}=0

=>(125+c)_/16=0

=>c=-125

so function is y=(5x²-125)_{/((x+3)(x-3))}

rational function y=(5x²-125)_{/((x+3)(x-3))} satisfies the given conditions.

There is no unique answer