Oblique Asymptotes Oblique asymptotes are straight lines that are not parallel to the axes that functions {curves} approach infinitely closely. They occur in rational functions in which the degree of the numerator polynomial exceeds the degree of the denominator polynomial by exactly 1. To determine the equation of any 0A. divide the denominator into the numerator using long division. Egl: Determine any asymptotes for the following function _3x3+10x+5 I") 3x+ 4 x+2 3x+4)3x2+10x+5 .'.f(x)=x+2 3x2+4x 0i:2 +6x+5 6x+8 3 3 This means that is the 0A. 3x + 4 When x is large and positive the difference between the function and the O.A. is represented by; x+2 - - 3 - (x+2) =-3 3x +4 3x + 4 The difference is negative and approaches from below. When x is large and negative the difference between the function and the O.A. is represented by; 3 x+2 -. - (x+ 2) = -- 3 3x + 4 3x + 4 The difference is positive and approaches from above. 180Y 16.0 14.0 12.0 10.0 8.0 6.0 40 2.0 4.0 23.0 -2.0 -10 2.0 10 -XM 2.0 3.0 4.0 4.0 6.0 -8.0 -10.0 -12.0 -14.0 -16.0 -18.0 ann