Simplifying Polynomials
Even, odd, or neither?
Max/Min, Inc./Dec., Domain/Range, etc.
ARoC
100
Simplify this polynomial and write it in standard form
(2x-5)+(x^2-2x)
x^2-5
100
Is this graph even, odd, or neither?
Even!
100
State all relative maximum and minimum(s) of this graph
Relative max: (-2, 16) and (2,16)
Relative min: (0,0)
100
Find the ARoC of this graph on [0,2]
a = 0, b = 2
f(a)=4, f(b)=-4
(-4 -(4))/(2-0)=-4
200
Simplify this polynomial and write it in standard form
(x^2-5x+4)-(3x^2+6x-6)
-2x^2-11x+10
200
Is this graph even, odd, or neither?
Odd!
200
What is the end behavior of this graph?
x -> -oo, f(x) ->0
x -> oo, f(x) ->0
200
Find the ARoC of this function on [2,10]
f(x)=10x-12
ARoC = 10
300
Simplify this polynomial and write it in standard form
(2x-3)(x+5)
2x^2+7x-15
300
Is this function even, odd, or neither?
f(x)=x^5-3x^3+8
Neither!
300
What is the domain and range of this graph?
Domain:
(-oo,oo)
Range:
(0,oo)
300
Find the average rate of change of this function on [3,5]
f(x)=2x^2-x
a = 2, b = 5
f(a)=15, f(b)=45
(45-15)/(5-3)=15
400
Simplify this polynomial and write it in standard form
(x^2+5x-1)(8x^2-9x+1)
8x^4+31x^3-52x^2+14x-1
400
Is this function even, odd, or neither?
f(x)=5x^4-3x^2+1
Even!
400
When is the graph increasing? When is it decreasing?
Increasing:
(-oo,0) and (2,oo)
Decreasing:
(0,2)
400
Find the average rate of change of this function on the interval [-3, 3]
f(x)=3/x-x
a = -3, b = 3
f(a)=2, f(b)=-2
(-2-2)/(3-(-3))=-4/6=-2/3 or .667