Block Directions: For each of the following, determine if the given rational function has a horizontal asymptote. If it does, write the equation of the horizontal asymptote. 1. f (x) = 3x -1 2. g (x) *+ 2x'+2+4 3. hix)= 3x -2x'-1 2x3 + 3x + 7 5x +7x+8 x'-6 Horizontal Asymptote: Y or N Horizontal Asymptote; Y or N Horizontal Asymptote: Y or N If Yes, Equation: If Yes, Equation: If Yes, Equation: 6x' +2x+3 4. k(x) = 5. r(x)= (2x-1) (3x +6) 2x -1 1x+4 6. 9(x)= (x] - 3) (x+3)(x-6) 3x +4x1 +7 Horizontal Asymptote: Y or N Horizontal Asymplute: Y or N Horizontal Asymptote: Y or N If Yes, Equation: If Yes, Equation: If Yes, Equation: 7. p(x)= (3x- 1] 8. p=(x-2) (4-x) 2x3 +3x+5 9. 8 (x ) (217 +3 )' (x-4) (x+3) (x* + 5 ) (x-2) Horizontal Asymptote: Y or N Horizontal Asymptote: Y or N Horizontal Asymptote: Y or N If Yes, Equation: If Yes, Equation: If Yes, Equation: Directions: Write limit statements for the end behavior of the following rational functions. 10. y = - 2x' -5x+6 (4x + 3)3 6x' +10x' -4x-12 11. y= (3x -1)(2x + 3) 12. y =- (x-1) Left: Left : Loft: Right: Right: Right: 1.7 Rational Functions and End Behavior