Login or Sign Up

Ask a New Question

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

-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)

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

Did you know?

Did you know that a reciprocal function is a type of rational function that can be represented by the equation f(x) = 1/x? To meet the given conditions of a vertical asymptote at x = -4 and x = 2, we can determine that the equation of the reciprocal function would be f(x) = k/(x+4)(x-2), where k is a constant. The presence of these factors in the denominator ensures that the function's value approaches infinity as x approaches -4 or 2. Additionally, the horizontal asymptote at y = 0 can be achieved by setting k = 1. By examining the given conditions, it becomes clear that the function should be positive when x belongs to the interval (-4, 2) and negative when x belongs to the intervals (-∞, -4) or (2, 8). Understanding these conditions helps us construct a reciprocal function that satisfies them.