Use the rational functions in problems 1 and 2 below to answer the following: (a) find the domain of the function; (b) find any holes the graph may have; (c) find the vertical asymptote(s) of the function; (d) find the horizontal and/or slant asymptote, if possible; (e) determine x- and y-intercepts; (f) use the previous information to graph the rational function. 1) ()=²+6/²2

2) ()=²4+4/3

Write an equation that describes the following variation problem. 3) varies directly with the square of . =45 when =3. Solve the following variation problem. 4) varies inversely with the cube of . If =1024 when =4, find when =2. For problems 3-5 use the following system of equations and find the solution using the specified methods { 3+2=5 24=2 5) Find the solution to the above system of equations using the substitution method. 6) Find the solution to the above system of equations using the elimination/addition method. 7) Find the solution to the above system of equations using the graphing method.

Answer the following systems of equations with whichever method you prefer.

9) { 23=5 46=2 10)

{+=2 2+=

=6

11. Without graphing or solving the following, determine if the solutions to the equations will have one solution, no solution, or infinitely many solutions a. {=2/3+5 =1/75

b. { =4/5+5 5=4+25