HW Answers: D: {x|x ≠ -5} VA: none Holes: (-5, -10) HA: none Slant: y = x – D: {x|x ≠ -1, 2} VA: x = 2 Holes: (-1, 4/3) HA: y = 2 Slant: None.

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HW Answers: D: {x|x ≠ -5} VA: none Holes: (-5, -10) HA: none Slant: y = x – 5 2 2 D: {x|x ≠ -1, 2} VA: x = 2 Holes: (-1, 4/3) HA: y = 2 Slant: None

HW Answers: D: {x|x ≠ 4,1} VA: x = 4, 1 Holes: none HA: y = 1 Slant: none D: {x|x ≠ 2, 6} VA: x = 6 Holes: (2, -1/4) HA: y = 0 Slant: none

HW Answers: D: {x|x ≠ -3, -1} VA: x = -3, -1 Holes: none HA: y = 2 Slant: none D: {x|x ≠ -2, -4} VA: x = -4 Holes: (-2, -6) HA: y = 3 slant: none

HW Answers: D: {x|x ≠ -1} VA: x = -1 Holes: none HA: y = 0 Slant: none

Steps for graphing Rational Functions 1) Find zeros of P(x) 2) Find zeros of Q(x) 3) Common Zeros holes Remaining Zeros of Q(x) Vertical asymptotes Remaining Zeros of P(x) x-intercepts 4) Find Horizontal asymptotes by studying the limit as x approaches , if none find the slant asymptote 5) Find the y-intercept by replacing x with zero. 6) Use sign analysis in the intervals separated by vertical asymptotes and x-intercepts 7) Sketch the graph. It will not cross vertical asymptotes. It can cross horizontal asymptotes but will approach it.

Ex1) Sketch the graph of the function: Slant: x y

Ex2) Sketch the graph of the function: Slant: x y

Ex3) Sketch the graph of the function: Slant: x y

Sneedlegrits: HW: Graphing Rational Functions