State the equation of a reciprocal function that meets the following conditions by justifying your choices:

Question

-vertical asymptote at x= -4 and x=2
-horizontal asymptote at y=0
-positive when x E (-4, 2) and negative when
x E (-infinity, -4) U (2,8)

Answer 1

start with
y = 1/((x+4)(x-2))
That's negative on (-4,2) so make it
y = -1/((x+4)(x-2))
Done.
check the graph at wolframalpha.com