Homework Review

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

41)lmx: 17, 27,lmn: -10, 24

42) lmx: 2, amx: 2

43) lmn: -3.2, amn:-3.2, amx: 3

44) lmx: 3.1, lmn: -3.1, amx: 3.1, amn: -3.1

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) Even78) even

80) Odd 82) neither

84) Neither

86) Even

88) Odd

90) neither

4.2: polynomial functions and models

November 6, 2009

Objectives

• Understand the graphs of polynomial functions.

• Evaluate and graph piecewise defined 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 Possible intercepts

Possible turning points

1

2

3

4

5

6

7

8

9

10

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

– 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

What is the degree and what is the sign of a?

• Try these…

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

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

x -5 -4 -3 -2 -1 0 0 1 2 2 3 4 5

y

Your assignment

• P. 268- 273– 9-18 – 36-38– 67-73