F(x)=-3/x^2+4
Graph all vertical and horizontal asymptotes of the rational function.
The vertical asymptote occurs at x = 0 since the function is undefined at this point.
To find the horizontal asymptote, we can examine the behavior of the function as x approaches positive and negative infinity. As x approaches positive infinity, the term -3/x^2 approaches 0, so the function approaches 4. As x approaches negative infinity, the term -3/x^2 also approaches 0, so the function approaches 4. Therefore, the horizontal asymptote is y = 4.
So the graph of the rational function F(x) = -3/x^2 + 4 has a vertical asymptote at x = 0 and a horizontal asymptote at y = 4.