HW Answers: x2 – 16 D: {x|x ≠ -4} VA: none Holes: (-4, -9) x – 4 2 2 D: {x|x ≠ ±1} VA: x = 1 Holes: (-1, 3/2)

HW Answers: D: {x|x ≠ 3,1} VA: x = 3, 1 Holes: none D: {x|x ≠ -1, -3} VA: x = -3 Holes: (-1, 3/2)

HW Answers: D: {x|x ≠ -4, -1} VA: x = -1 Holes: (-4, 8) D: {x|x ≠ -5} VA: x = -5 Holes: none

2.7

  x y x y 1 10 100 x y -1 -10 -100

If there is a horizontal asymptotes it will fit one of the three following cases:  

 

 

Find the horizontal asymptote: Exponents are the same; divide the coefficients Bigger on Top; None Bigger on Bottom; y=0

SLANT/OBLIQUE ASYMPTOTES If the degree of the numerator is exactly one more than the degree of the denominator, then there is not a horizontal asymptote, but an oblique or slant asymptote. The equation is found by doing long division and the quotient is the equation of the slant or oblique asymptote ignoring the remainder. degree of top = 3 degree of bottom = 2 Slant asymptote at y = x + 5

Example 1: Find the domain, vertical, horizontal or slant asymptotes and any holes.

Example 2: Find the domain, vertical, horizontal or slant asymptotes and any holes.

Example 3: Find the domain, vertical, horizontal or slant asymptotes and any holes.

HW: Finding Asymptotes and Holes 2 Sneedlegrit: Find the domain, vertical, horizontal or slant asymptotes and any holes. x y HW: Finding Asymptotes and Holes 2