AFM Day 4 Rational Functions Notes Rational --- FRACTIONAL!!! Vertical Asymptotes (VA) Dotted vertical lines the graph approaches FACTOR denominator IF POSSIBLE but never touches (x = #) Set denominator (factors) = 0, Solve for x Horizontal Asymptotes (HA) where m = degree of numerator End behavior of the graph n = degree of denominator Dotted horizontal line Y = # HA = (graph usually does not intersect, but can) At most one horizontal asymptote Asymptote (SA) IF FACTORED LOOK AT ORIGINAL PROBLEM Oblique line (neither vertical nor horizontal) Use long division or synthetic to find equation of . Slant Asymptote & DISREGARD REMAINDER If there is NO horizontal asymptote and m>n by one degree FACTOR everything and reduce common factors Hole Point of discontinuity (open circle) set common factor = 0 to solve for x, plug that When there is a common FACTOR reduced value into simplified rational equation to obtain ordered pair (hole) X intercepts set numerator = 0 and solve for x Points on graph that lie on x-axis (or let y = 0 and solve for x) let x = 0 and solve for y Y intercepts Points on the graph that lie on the y-axis Examples: Identify the characteristics of each rational function. If the characteristic does not exist, write NONE. 1. 2.
AFM Day 4 Rational Functions Notes Rational --- FRACTIONAL!!! Vertical Asymptotes (VA) Dotted vertical lines the graph approaches FACTOR denominator IF POSSIBLE but never touches (x = #) Set denominator (factors) = 0, Solve for x Horizontal Asymptotes (HA) where m = degree of numerator End behavior of the graph n = degree of denominator Dotted horizontal line Y = # HA = (graph usually does not intersect, but can) At most one horizontal asymptote Asymptote (SA) IF FACTORED LOOK AT ORIGINAL PROBLEM Oblique line (neither vertical nor horizontal) Use long division or synthetic to find equation of . Slant Asymptote & DISREGARD REMAINDER If there is NO horizontal asymptote and m>n by one degree Hole FACTOR everything and reduce common factors Point of discontinuity (open circle) set common factor = 0 to solve for x, plug that When there is a common FACTOR reduced value into simplified rational equation to obtain ordered pair (hole) X intercepts set numerator = 0 and solve for x Points on graph that lie on x-axis (or let y = 0 and solve for x) Y intercepts let x = 0 and solve for y Points on the graph that lie on the y-axis Examples: Identify the characteristics of each rational function. If the characteristic does not exist, write NONE. 1. 2.
packet_unit_1_-_revised_f2017.docx