Show:
End Behavior
Intercepts
Multiplicity
Classifying Polynomials
Sketching Graphs
100

What is the end behavior of f(x)= x^3?

As x--> -∞, f(x)---> -∞

as x--> +∞, f(x)---> +∞

100

To find the x-intercepts of a function, you must apply the _________ property 

Zero Product Property

100

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

100

Classify this terms by it's degree and number of terms


5x^2-6

Quadratic Binomial

100

What happens at the x-intercept with an even multiplicity?

The graph will bounce off the intercept

200

What is the end behavior of f(x)= 1/3 (x+73)^2 (x+2)?

As x--> -∞, f(x)---> -∞

as x--> +∞, f(x)---> +∞

200

What are the x-intercepts of this factored polynomial?

(x+1)(x-2)

x=-1 x=2

200

What are the multiplicities for the following zeroes

(x-5)(x-2)^2

5 occurs once, 2 occurs twice

200
Put this polynomial in standard form...


5 - x^3 + 3x

x^3+3x-5

200

What happens at an x-intercept when solution has an odd multiplicity

The graph passes through the x-intercept

300

What is the end behavior of -x^28 + x^4?

As x--> -∞, f(x)---> -∞

as x--> +∞, f(x)---> -∞

300
What is the x intercept of f(x)= x^3 (x-5)?
What is 0 and 5?
300

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

300

Classify the polynomial by degree and number of terms...

-12

Constant Monomial

300

The number of turning points in a polynomial will always be one less than the....

Degree of the polynomial

400

What is the end behavior of -71x^77 + x^50 + 123?

As x--> -∞, f(x)---> +∞

as x--> +∞, f(x)---> -∞

400
What is the x intercept of f(x)= 2 (x+5) (x-3) (x+7)?
What is -5, 3, -7?
400

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

400

Classify the polynomial by degree and number of terms


x^4-2x+6

Quartic Trinomial

400

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)

500

What is the end behavior of (2x^6) (720x^8)?

As x--> -∞, f(x)---> +∞

as x--> +∞, f(x)---> +∞

500
What is the y-intercept of -3x^2 (2x+2)?
What is 0?
500

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

500

Classify the following by degree and number of terms


x^5+4x^3-2x^2+7

Quintic Polynomial

500

Graph the following polynomial


(x-4)(x+2)

(Image)