Chapter 3.5 : Making Connections With Rational Functions and Equations

a) f(x) = (x^2 - x - 6) / (x+2)

• Restriction : x+2 ≠ 0

                                          x≠ -2

• Domain : {xɛR , x ≠ -2}
• Equation of vertical asymptote : none

                    Reason : (x^2 - x - 6) / (x+2) = [(x-3)(x+2)] / (x+2)

                                                          So, [(x-3)(x+2)] / (x+2)

                                                                  x-3 = 0 

                                                                      x= 3

• f(-2) = undefined
• Graph : 

The graph is discontinuous at x= -2 , while the point is (-2 , -5)

* N = numerator , D = denominator , HA = Horizontal asymptote , LC = Leading coefficient

Remember : N< D is HA  = 0

                   N> D has no HA 

                   N = D is,  HA = y = LC of N / LC of D