Graph and label the following two functions: f(x)=(x^2+7x+12)/(x+4) g(x)=(-x^2+3x+9)/(x-1) 1. Describe the domain and range for each of these functions. 2. Determine the equation(s) of any asymptotes found in the graphs of these functions, showing all work. 3. Discuss the conditions needed for a rational function to contain a slant asymptote.

Answer 1

f is any x except x=-4, g is any x except x=1

range, consider f
f when x=-inf ; f= (inf)^2/inf
when x=+inf; f= (inf)^2/inf

so range of f is -inf to inf

consider g
when x=-inf; g-inf^2/-inf= -inf
x=+inf; g= inf^2/inf= inf

range is -inf to inf