End Behavior
What is the end behavior of f(x)= x^3?
As x--> -∞, f(x)---> -∞
as x--> +∞, f(x)---> +∞
To find the x-intercepts of a function, you must apply the _________ property
Zero Product Property
To find the number of times each zero occurs, you can look at the factors' _______
A. Exponent
B. Sign
C. Y-Intercept
D. Number of turning points
Exponent
Classify this terms by it's degree and number of terms
5x^2-6
Quadratic Binomial
What happens at the x-intercept with an even multiplicity?
The graph will bounce off the intercept
What is the end behavior of f(x)= 1/3 (x+73)^2 (x+2)?
As x--> -∞, f(x)---> -∞
as x--> +∞, f(x)---> +∞
What are the x-intercepts of this factored polynomial?
(x+1)(x-2)
x=-1 x=2
What are the multiplicities for the following zeroes
(x-5)(x-2)^2
5 occurs once, 2 occurs twice
x^3+3x-5
What happens at an x-intercept when solution has an odd multiplicity
The graph passes through the x-intercept
What is the end behavior of -x^28 + x^4?
As x--> -∞, f(x)---> -∞
as x--> +∞, f(x)---> -∞
What are the multiplicities for each zero?
X^3(x-1)^4(x+2)
x=0 occurs three times, x=1 occurs fours times, x=-2 occurs once
Classify the polynomial by degree and number of terms...
-12
Constant Monomial
The number of turning points in a polynomial will always be one less than the....
Degree of the polynomial
What is the end behavior of -71x^77 + x^50 + 123?
As x--> -∞, f(x)---> +∞
as x--> +∞, f(x)---> -∞
What are the multiplicities for the function?
x^3(2x+3)(x-1)
x=0 occurs three times
x=-3/2 occurs once
x=1 occurs once
Classify the polynomial by degree and number of terms
x^4-2x+6
Quartic Trinomial
Graph the following polynomial
x^3+5x^+6x
(Hint: Factor the polynomial and use your knowledge about end-behavior, zeroes and multiplicities to sketch)
(Image)
What is the end behavior of (2x^6) (720x^8)?
As x--> -∞, f(x)---> +∞
as x--> +∞, f(x)---> +∞
What are the x-intercepts of the following polynomial? (Hint: You will need to factor first)
x^4+5x^3+6x^2
x=-3 occurs once
x=-2 occurs once
x=0 occurs twice
Classify the following by degree and number of terms
x^5+4x^3-2x^2+7
Quintic Polynomial
Graph the following polynomial
(x-4)(x+2)
(Image)