Putting It All Together - Graphing Rational Functions 1.2 2006/04/24 01:51:49 GMT-5 2006/05/01 08:52:16.760 GMT-5 Pradnya Vinay Bhawalkar pradnyab89@gmail.com Kim Dodge Johnston kim.johnston@fortbend.k12.tx.us Pradnya Vinay Bhawalkar pradnyab89@gmail.com asymptote domain Function Graphing hole horizontal asympote intercepts Rational slant asymptote vertical asymptote zero Graphing rational functions. When graphing rational functions, find the domain, vertical asymptotes, slant asymptotes, holes (if any), horizontal asymptotes, vertical asymptotes, zeros, and y-intercept. To practice, graph each rational function. State the domain, hole(s), VA (vertical asyptote(s)), HA(horizontal asymptote), SA(slant asymptote), zeros, and y-intercept(y-int). Use graph paper. r x x 1 x x 4

Domain: -4 -4 0 0 Hole: None VA: x0, x-4 HA: y0 SA:None Zero: (-1,0) Y-int: None h x 2 x 2 x 3 x 1 x 2

Domain: -2 -2 1 1 Hole: None VA: x-2, x1 HA:None SA: y 2 x 8 Zeros: (0,0), (3,0) Y-int: (0,0) f x 3 x 3 2 x 4

Domain: -2 -2 Hole: None VA: x-2 HA: y32 SA: None Zero: (-1,0) Y-int: (0,34) g x 6 x 2 x 6

Domain: -2 -2 3 3 Hole: None VA: x-2, x3 HA: y0 SA: None Zeros: None Y-int: (0,-1) h x 2 x 4 x 1

Domain: 1 1 Hole: None VA: x1 HA: y2 SA: None Zero: (-2,0) Y-int: (-2,0) t x 3 x x 2 4

Domain: Hole: None VA: None HA: y0 SA: None Zero: (0,0) Y-int: (0,0) f x x 2 4 x 2 4

Domain: -2 -2 2 2 Hole: None VA: x-2, x2 HA: y1 SA: None Zeros: None Y-int: (0,-1) f x x x 2 2

Domain: -2 -2 Hole: None VA: x-2 HA: y0 SA: None Zeros: (0,0) Y-int: (0,0) f x 5 x 2 x 3

Domain: -3 -3 Hole: None VA: x-3 HA: None SA: y 5 x 15 Zeros: (0,0) Y-int: (0,0) f x x 3 x 2 1

Domain: Hole: None VA: None HA: y0 SA:None Zeros:(3,0) Y-int: (0,-3)