Review:

3. What is an asymptote?

4. What is an end behavior model?

Answers:3. 96 ft/s6.

9. -1512. 015. Does not exist18. 821. -1/224. 227. 030. Possible Answer [-4.7,4.7] [-15,15]33. 036. -138a,d,e,f,g,h,i: True b,c: False

47. y = x - 1, x≠150a. 4 b. -21 c. -12 d. -7/351b. c. No54b. c. Yes55b(-2π,0)∪ (0,2π) c. 2π d. -2π61. 064a. y = gt2

g = 1.25 b. 5m/s c. 10 m/s

Vocabulary:Horizontal Asymptote: Occurs if or for any line y = b

Vertical Asymptote: Occurs if or for any line x = a

End Behavior Model: Take two different functions that are being divided and use limits to estimate what value they will approach.

Properties of Limits as x ±∞If L, M, and k are real numbers and

Ex 1: Find the horizontal asymptotes for

Ex 2: Find

Ex 3: Find

c. Does the limit as x approaches 2 exist? Why or why not?

Ex 4: Find the end behavior for:a) f(x) = 4x5 - 5x3 + 9x - 11

b) g(x) = -4x2 + 8x3 - x4

c) h(x) = 6x-4 + 9x-2 + 8x-1

Ex 5: Find the end behavior for:

a) f(x) = 5x2 - 10x + 25 b) g(x) = 4x3 - 8x x3 + 9x

x2 + 5

Ex 6: Find the left and right behavior for

a) f(x) = ex - 2x b) g(x) = x2 + sin x

Assignment: p76 #3-36(x3), 43, 46, 54-55, 59, 65, 68