Please give me correct answers Find all zeros and vertical a

Please give me correct answers!

Find all zeros and vertical asymptotes of the rational function f(x) = x^2 - 16/x^2 + 16. If there is more than one answer, enter your answers as a comma separated list. If there is no solution, enter NONE. Do not leave a blank empty. The function has x-intercept(s) at x = The function has y-intercept(s) at y = The function has vertical asymptote(s) when x = The function has horizontal asymptote(s) when y =

Solution

given f(x)=y=(x²-16)/(x²+16)

a) for x intecept, y =0

=>(x²-16)/(x²+16)=0

=>(x²-16)=0

=>x=-4, x=4

b) for y intercept , x =0

y=(0²-16)/(0²+16)

y=-16/16

y=-1

c) no vertical asymptotes

d) horizontal asymptote

y =lim_x->(x²-16)/(x²+16)

y =lim_x->(x²(1- 16/x²))/(x²(1 + 16/x²))

y =lim_x->(1- 16/x²)/(1 + 16/x²)

y =(1-0)/(1+0)

y =1