h(x)=(3x^2+10x-8)/(x^2+4) Graph the function.

We are asked to graph the function y=(3x^2+10x-8)/(x^2+4) :
Factoring the numerator gives us:
y=((3x-2)(x+4))/(x^2+4)
There are no vertical asymptotes. Since the degree of the numerator agrees with the degree of the denominator, the horizontal asymptote is y=3.
The x-intercepts are 2/3 and -4. The y-intercept is -2.
The first derivative is y'=(-10(x^2-4x-4))/((x^2+4)^2) . Using the first derivative test the function decreases for x<2-2sqrt(2) , has a minimum at x=2-2sqrt(2) , increases on 2-2sqrt(2)2+2sqrt(2) .
The graph: