Unit 13 Test Review
Higher Degree Polynomials
name ___________________________________
period ______________
_____1. Which of the following is the graph of f  x    x  1
2
 x  2 ?
Given the graph below, answer the following questions.
2. What is the Domain? ____________________
3. What is the Range? _____________________
4. Is the Leading Coefficient positive or negative? _____________
5. Is the degree odd or even? ____________________
6. End Behavior _____________________________________
_____________________________________
7. What are the roots? (Include multiplicities)_______________________________________________________________
___________________________________________________________________________________________________
8. What are the factors? ______________________________________________
9. Identify the zeros and where they appear on the graph for the following function. f ( x)  x
2
 x  2   x  3
3
(does it bend at the x  axis , touch the x  axis and turn around, or does it cross the x  axis )
x
______ ;____________________________________________
x
______ ;____________________________________________
x
______ ;____________________________________________
10. Identify the leading coefficient, degree and end behavior of the function
Leading Coefficient: _____________
P  x   5x4  6x2  6
Degree : _________________
As x   , P( x)  ____________
End Behavior:
As x   , P( x)  ___________
11. Which one of these functions might have the given graph? Explain why. ____________________________________
_____________________________________
_____________________________________
_____________________________________
_____________________________________
Is the leading coefficient positive or negative, is the degree even or odd, state the end behavior.
LC: _______ Degree: _________
End Behavior As
x   , P( x)  ____________ As x   , P( x)  ___________
12. The polynomial
f  x   3x4  9x2  6x has a zero at x  1 . Factor f completely.
Write the polynomial of the given graph in factored form. Is the leading coefficient positive or negative, is the degree even or
odd, state the end behavior.
13.
f  x   _______________________________
LC: __________ Degree: _________
End Behavior
As x   , P( x)  ____________
As x   , P( x)  ___________
14.
f  x   ________________________________
LC:______________ Degree: __________
End Behavior
As x   , P( x)  ____________
As x   , P( x)  ___________
15. Use the equation,
f ( x)  x5  x4  3x3  5x2  2x
to answer the following questions. Given Factors:
 x  2 x  1
MUST SHOW WORK FOR CREDIT
list the POSSIBLE zeros ______________________________________________________________________________
List all linear factors _________________________________________________
List the actual zeros ____________________________________________________________________________
****state the multiplicity*****
Sketch the approximate graph
16.Use the equation,
Given Factors:
f ( x)  2x6  x5  20x4  29x3 12 x2
to answer the following questions.
 x  4 x  1
MUST SHOW WORK FOR CREDIT
list the POSSIBLE zeros ______________________________________________________________________________
List all linear factors _________________________________________________
List the actual zeros ____________________________________________________________________________
****state the multiplicity*****
Sketch the approximate graph