Polynomial Functions
Polynomial Graphs
Factoring/Solving
Rational Functions
100
Is it possible to have a polynomial of degree 7 without any x-intercepts? Why or why not?
It is not possible to have one because the polynomial has an odd degree, therefore the end behavior is opposite so at some point the function MUST cross the x-axis.
100
What is the degree and leading coefficient?
f(x)=-5x^5+3x^3-3x+1
D:5
LC:-5
100
Factor the polynomial:
x3+7x2+10x
x(x+5)(x+2)
100
Find the Domain, VA, HA, Holes, Xint, and the Yint of the following function. f(x)= (2.5x+1800)/x
What is domain: all reals except 0, VA: at x=0, HA: at y=2.5, Holes: none, xint: at x=-720, yint: none?
200
g(x)= -x^5 +5x^3 -4x
Answer the following: Degree, LC, End Behavior, Max # of X-intercepts, Max # of Turning Points
What is Degree: 5
LC: -1
EB:Up, Down
Max X's: 5
Max TP's: 4
200
What do we know about the leading term of this graph?
Degree: Even
L.C.: Positive
200
Factor the polynomial:
9x3+6x2-3x
3x(3x-1)(x+1)
200
f(x)=(80,000p)/(100-p) Find the domain, VA, HA, Holes,
P-ints, and the Y-int.
What is domain: all reals except 100, VA: at p=100, HA: at y=-80,000, Holes: none, P-ints: at p=0, Y-int: y=0
300
Is it possible to have a polynomial function with degree 10 that falls to the left and falls to the right? Why or why not?
What is yes it is possible because with an even degree polynomial, the end behaviors MUST be the same.
300
Describe end behavior (using infinity)
As x 
As x
300
Factor the polynomial and find the zeros:
3x3+12x2-3x=12
x=-4,-1,1
300
f(x)= 1/x
Find the domain, VA, HA, Holes, Xints, and Yint.
What is domain: all reals except 0, VA: at x=0, HA: at y=0, Holes: none, Xint: none, Yint: none?
400
f(x)=x(x^2 -4) Find the following: Degree, LC, End Behavior, Max # of X-intercepts, and the Max # of Turning Points
What are Degree: 3
LC: 1
EB: Down, Up
Max X's: 3
Max TP's: 2
400
Find the x and y intercepts of the function
f(x)=-2(x+1)(x-2)(x+3)
x intercepts: -1, 2, and -3
y intercept: 12
400
Factor the polynomial to find the zeros. You may need to use the quadratic equation.
12x3=60x2+75x
x=0, (5 +/- 5sqrt2) /2
400
Write a function with the following characteristics. A hole at x=3 and a HA at y=6 There are many possible answers.
What is 6x/(x-3)?
500
Is it possible to have a polynomial function of degree 9 with 3 valleys and 3 hills? Why or why not?
What is yes, it is possible because there can be up to 8 turning points an 3 valleys and 3 hills creates opposite end behavior.
500
Describe the following for the graph:
Leading coefficient, degree, zeros, y intercept
L.C.: positive
Degree: even
Zeros: -3, 2, 5
Y-int: -2
500
Factor the polynomial to find the zeros.
x3+1=x2+x
x=-1,1
500
Find a function with the following characteristics. An xintercept at x= -7, a VA at x=9, a HA at y=3, and a hole at x=-2
What is 3(x+7)(x+2)/(x-9)(x+2)?