Question

Write the equation of a rational function g(x) with vertical asymptotes at x = -3 and x = 3 , a horizontal asymptote at y = -4 and with no x intercept.

Answer 1

Answer:

The equation for rational function for given asymptotes is

f(x)=(-4x^2-6)/{(x-3)(x+3)}

Step-by-step explanation:

Given:

vertical Asymptotes at x=3 and x=-3 and a horizontal asymptote at

y=-4 i.e parallel  to x axis.

To find:

equation of a rational function i.e function in form p/q

Solution;

the equation should be in form of p/q

Numerator :denominator.

Consider f(x)=g(x)/h(x)

as vertical asymptote are x=-3 and x=3

denominator becomes, (x-3) and (x+3)

for horizontal asymptote to exist there should have same degrees  in numerator and denominator which of '2'

when g(x) will be degree '2' with -4 as coefficient and dont have  any real.

zero.

By horizontal asymptote  will be (-4x^2 -6)

The rational function is given by

f(x)=g(x)/h(x)

={(-4x^2-6)/(x-3)(x+3)}.