Factoring
Operations with Functions
Graphs
Features of Fuctions
100
Factor completely to find the zeroes:
f(x)=x^3-3x^2-x+3
x=3, 1, -1
100
Use Synthetic Division to divide the polynomials:
(x^4-9x^3+10x^2+46x+16)÷(x-6)
x^3-3x^2-8x-2+4/(x-6)
100
Find the zeros of the function:
x=-4, -2, 0, 3
100
Determine the end behavior of the function:
f(x)=-x^3+4x^2-x+7
As x->-∞, f(x)->
As x-> ∞, f(x)->
As x->- ∞, f(x)->∞
As x-> ∞, f(x)->-∞
200
Factor:
27x^3-8
a. (3x-2)(3x^2+6x+4)
b. (3x+2)(9x^2-6x+4)
c. (3x-2)(9x^2+6x+4)
d. (3x+2)(3x^2-6x+4)
c
200
Use the Factor Theorem to determine if x = 3 is a root of x^3+5x^2-50 .
Root? (Circle)
Yes / No
No
200
Label the graphs as even, odd, or neither:
Neither, odd, even.
200
Determine which of the following are even functions:
I. f(x)=3x^5+x
II. f(x)=4x^3-6x^2
III. f(x)=7x^6+5x^4-3
a. I only
b. I and III
c. II only
d. III only
d
300
Factor completely:
25x^4-36
(5x^2+6)(5x^2-6)
300
Use the Factor Theorem to write the polynomial, f(x), with the given zeros:{3, 5, 0}
a. What are the factors?
b. Distribute the above factors to find f(x).
a.
x(x-3)(x-5)
b.
x^3-8x^2+15x
300
Which is the equation of the following function?
a. f(x)=x^2+3
b. f(x)=(x+3)^2
c. f(x)=x^2-3
d. f(x)=(x-3)^2
d
300
Describe the translations of f(x)=-1/3(x-4)^3 from the parent function f(x)=x^3 .
Choose all that apply.
a. g(x) is shifted four units to the right of f(x)
b. g(x) is shifted four units up from f(x)
c. g(x) is reflected over the x-axis f(x)
d. g(x) represents a vertical stretch compared to f(x)
e. g(x) represents a vertical shrink compared to f(x)
a, c, e
400
Solve for x:
x^3-9x^2+20x=0
x=0, 5, 4
400
Complete the indicated operations using the given functions:
f(x)=4x-5
g(x)=x^2+2x-6
h(x)=2x^2-x+3
1. g(3)
2. f(3t)+3(g(t)
3. g(x)+h(x)
1. 9
2.
3t^2+18t-23
3.
3x^2+x-3
400
Use the zeros to sketch the polynomial function.
f(x)=x(x+4)(x-5)
400
Determine the intervals of increasing and decreasing for the following function:
Increasing:
(-3, 0)U(3, ∞)
Decreasing:
(-∞, -3)U(0,3)
500
If is a parabola that has been reflected over the x-axis, shifted down 4 units and left 1 unit, sketch the graph of and determine its equation.
-(x+1)^2-4
500
Identify the maximums and minimums of the graph. Give your answer as points.
Maximums:(-6, 5), (1, 4), (7, 7)
Minimums: (-1, -2), (4, 0)