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Homework Review. P. 251-256 12-16, 40-44. 12) in (-∞, -1], de [-1, ∞) 13) in (- ∞, 2], [1, ∞), de [-2, 1] 14) in (- ∞, -2] , [0, 1], de [-2, 0], [1, ∞] 15) in [-8, 0], [8, ∞), de (- ∞, 8], [0, 8] 16) in (- ∞, 0], de [0, ∞). 40) lmx : 0, lmn : -5, no amx , amn : 5

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p 251 256 12 16 40 44
P. 251-25612-16, 40-44

12) in (-∞, -1], de [-1, ∞)

13) in (- ∞, 2], [1, ∞), de [-2, 1]

14) in (- ∞, -2] , [0, 1], de [-2, 0], [1, ∞]

15) in [-8, 0], [8, ∞), de (- ∞, 8], [0, 8]

16) in (- ∞, 0], de [0, ∞)

40) lmx: 0, lmn: -5, no amx, amn: 5

  • lmx: 17, 27,lmn: -10, 24
  • lmx: 2, amx: 2
  • lmn: -3.2, amn:-3.2, amx: 3
  • lmx: 3.1, lmn: -3.1, amx: 3.1, amn: -3.1
p 251 256 45 48 70 90 even
P. 251-25645-48, 70-90 even

45) lmx: 1, lmn: -1, amx: 1, amn: -1

46) lmx: 0.5, 2, lmn:-0.5, -2, amx: 0.5, 2, amn: -0.5, -2

47) lmn: -2, lmx: 1, 2, amn: -2, amx: 2

48) lmx: 2.5, lmn: 2, -12

Amn: -12

70)even 72) odd

74) Neither

76) Even 78) even

80) Odd 82) neither

84) Neither

86) Even

88) Odd

90) neither

objectives
Objectives
  • Understand the graphs of polynomial functions.
  • Evaluate and graph piecewise defined functions.
understand the graphs of polynomial functions
Understand the graphs of polynomial functions.
  • If a polynomial has a degree n, where n≥1, then it has…
    • at most, n x-intercepts
    • at most, n-1 turning points
n is even n 2
n is even, n ≥ 2
  • a>0: The graph rises both to the left and the right
  • a<0: the graph falls both to the left and right
n is odd and n 1
n is odd and n ≥1
  • a>0.. The graph falls to the left and rises to the right
  • a<0… the graph rises to the left and falls to the right
evaluate and graph piecewise defined functions
Evaluate and graph piecewise defined functions.
  • Remember piecewise linear functions?
  • These are very similar.
  • Key ideas:
    • Continuous: no breaks in the graph
    • Evaluate: find the solution at the given value of x
    • Solve f(x) = ?: solve for y at this value
evaluate and graph piecewise defined functions1
Evaluate and graph piecewise defined functions.

f(x)={ x2-15 if -5≤x<0

{2x-1 if 0≤x<2

{-(x2+1) if 2≤x<5

  • Evaluate at x= -1, 0, 1, 2
  • Is it continuous?
  • Solve for f(x) = 0
your assignment
Your assignment
  • P. 268- 273
    • 9-18
    • 36-38
    • 67-73