End Behavior
Zeros and Multiplicity
Multiplicity and their Effects
100
Describe the end behavior of the function f(x)=-2x2-16x-27
As x --> -∞, f(x) --> _____
As x--> ∞ , f(x) --> _____
As x --> -∞, f(x) --> -∞
As x--> ∞ , f(x) --> -∞
100
Identify the zeros and their multiplicity of the polynomial function f(x)=(x+2)(x-3)2(x+4)3
x=-2
x=3 multiplicity 2
x=-4 multiplicity 3
100
For each given zero, determine if the multiplicity is odd or even and the effect (bounces or crosses)
f(x)=(x+2)(x-4)2(x+3)3(x+1)2
x=-2
x=4
x=-3
x=-1
x=-2 odd multiplicity; crosses
x=4 even multiplicity; bounces
x=-3 odd multiplicity; crosses
x=-1 even multiplicity; bounces
200
Describe the end behavior of the function f(x)=5x3-2x2+4
As x --> -∞, f(x) --> _____
As x--> ∞ , f(x) --> _____
As x --> -∞, f(x) --> -∞
As x--> ∞ , f(x) --> ∞
200
Identify the zeros and their multiplicity of the polynomial function f(x)=-(x-2)4(x+2)2(x-1)
x=2 multiplicity 4
x=-2 multiplicity 2
x=1
200
For each given zero, determine if the multiplicity is odd or even and the effect (bounces or crosses)
f(x)=x(x+1)(x-2)(x+4)2(x-3)3
x=0
x=-1
x=2
x=-4
x=3
x=0 odd multiplicity; crosses
x=-1 odd multiplicity; crosses
x=2 odd multiplicity; crosses
x=-4 even multiplicity; bounces
x=3 odd multiplicity; crosses
300
Describe the end behavior of the function f(x)=2x(x-5)2(x+4)3
As x --> -∞, f(x) --> _____
As x--> ∞ , f(x) --> _____
As x --> -∞, f(x) --> ∞
As x--> ∞ , f(x) --> ∞
300
Identify the zeros and their multiplicity of the polynomial function f(x)=x(x+5)2(x-4)3
x=0
x=-5 multiplicity 2
x=4 multiplicity 3
300
For each given zero, determine if the multiplicity is odd or even and the effect (bounces or crosses)
x=-1
x=2
x=4
x=-1 odd multiplicity; crosses
x=2 even multiplicity; bounces
x=4 odd multiplicity; crosses
400
Describe the end behavior of the polynomial function graphed below
As x --> -∞, f(x) --> _____
As x--> ∞ , f(x) --> _____
As x --> -∞, f(x) --> ∞
As x--> ∞ , f(x) --> -∞
400
Identify the zeros and their multiplicity (odd or even) of the polynomial function graphed below
x=-3 (odd multiplicity)
x=-2 (even multiplicity)
x=1 (odd multiplicity)
400
For each given zero, determine if the multiplicity is odd or even and the effect (bounces or crosses)
x=-4
x=-2
x=0
x=3
x=-4 odd multiplicity; crosses
x=-2 even multicity; bounces
x=0 even multiplicity; bounces
x=3 odd multiplicity; crosses
500
Describe the end behavior of the polynomial function graphed below
As x --> -∞, f(x) --> _____
As x--> ∞ , f(x) --> _____
As x --> -∞, f(x) --> -∞
As x--> ∞ , f(x) --> ∞
500
Identify the zeros and their multiplicity (odd or even) of the polynomial function graphed below
x=-4 (even multiplicity)
x=-2 (even multiplicity)
x=-1 (odd multiplicity)
500
For each given zero, determine if the multiplicity is odd or even and the effect (bounces or crosses)
x=-3
x=-1
x=2
x=-3 even multiplicity; bounces
x=-1 even multiplicity; bounces
x=2 even multiplicity; bounces