-Assignment- 2.1 = 68(c-e), 73, 79, 80, & 85
2.2 = 1-8, 11, 22-36 even, 39, 45, 48, 63, 96, 102, 103(a-f)
-The Maximum number of intercepts for a Polynomial is the variables highest exponent.
extrema- relative minimums or maximums
Real Zeroes of Polynomial Functions-
1. x = a is a zero of the function
2. x = a is a solution of the polynomial equation f(x) = 0
3. (x-a) is a factor of the polynomial f(x)
4. (a,0) is an x-intercept of the graph of f
-Finding zeros of polynomial functions is closely related to factoring and finding x-intercepts
End Behavior
X -> 00 x -> -00
f(x) -> 00 f(x) -> 00
Example problem = 3x^5 - 7x^4 + 3x^3 - 2x + 1 = x -> 00 , f(x) -> 00
Intermediate Value Theorem - concerns the existence of real zeros of polynomial functions.
-theorem states that if (a, f(a)) and (b,f(b)) are two points on the graph of a polynomial functions such that f(a) can not = f(b), then for any number d between f(a) and f(b) there must be a number c between a and b such that f(c) = d
Helpful Video- http://www.youtube.com/watch?v=4TA5Zy8Hap8
-
-Leading Coefficient Test- Test used to determine whether the graph of a polynomial eventually rises or falls
No comments:
Post a Comment