What is the range of the function $g(x) = \frac{3x+1}{x+8} + \frac{2x-4}{x+8}$ ?
Simplify as
[ 3x + 1 + 2x - 4] / [ x + 8] =
[ 5x - 3 ] / [ x + 8]
This function has a horizontal asymptote at y = (the ratio of the coefficients on x ) = 5/1 = 5
The range is (-inf, 5) U (5, inf)