Ch : Graphs of Rational Functions

Identifying Asymptotes Vertical Asymptotes –Set denominator equal to zero and solve: x = value Horizontal Asymptotes –Degree of numerator < degree of denominator: y = 0 –Degree of numerator = degree of denominator: –Degree of numerator > degree of denominator: none!! **Instead, you possibly get a slant asymptote** Slant Asymptotes: numerator degree must be EXACTLY ONE GREATER than denominator degree –Long divide the numerator by the denominator, disregard the remainder y = quotient

Identify the Asymptotes Horizontal: y = 1 Vertical: x = 3

To graph 1.Graph the vertical asymptote(s) 2.Graph the horizontal asymptote (or slant asymptote) 3.Find at least three values on each side of the vertical asymptotes to put the picture together **Use the calculator to check** Note: Factor the numerator and denominator when possible. If a factor cancels out, then it is not an asymptote, but the function still cannot equal that value. There will be a hole instead.

1.Vertical Asymptote: 1-x = 0, so x = 1 2.Horizontal Asymptote: x = x, so 3.No S.A. 4.Points: X-424 Y -4-2

1.Vertical Asymptote: x-2 = 0, so x = 2 2. Horizontal Asymptote: x 2 > x, so none 3. S.A.: long divide, ignore remainder; 4. Points: X-2135 Y 810

1.Vertical Asymptote: x-3 = 0, so x = 3 but there is a hole at (-2, 3/5) 2. Horizontal Asymptote: x= x, so 3. S.A.: none 4. Points: X-4245 Y-.7132