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Algebra II
Name: __________________
Polynomial Functions Test Review
Part I: Polynomial Functions
For each function, state the degree, roots, domain, range, and whether it is even or odd.
1. h( x)  2 x5  3x  2
2. graph: g ( x)  x 4  x3  7 x 2  x  6
4
3
2
1
-6
-4
-2
2
4
6
-1
-2
-3
-4
Degree: _______
Even
Odd
Degree: _______
Even
Odd
# of Real Roots: _____________________
# of Real Roots: ______________________
# of Imaginary Roots: _________________
# of Imaginary Roots: _________________
Domain: _________
Domain: _________
Range: ___________
Range: __________
Maximum:_________________________
Minimum:_________________________
3. p( x)  x3  2 x 2  3x  5
2
Degree: _________
1
-6
-4
-2
2
4
6
# of Real Roots: ____________________
-1
-2
# of Imaginary Roots: _______________
-3
-4
Domain: ______________
-5
Range: _______________
-6
Even
Odd
4. What are the factors of the following graph?
5. If f (n)  n  3n , find f (3).
4
2
-5
5
-2
-4
6. If g ( x)  4 x 2  3 , find g (3).
Use synthetic division:
7. What is the solution set of the graph below?
4
2
-5
5
-2
-4
-6
8. What polynomial function has
x-intercepts x = 2 and x = -3?
9.What are the zeros of the following graph?
4
2
-5
5
-2
-4
10. Assuming the domain is all real numbers,
what is the range of y  x 2  9 ?
11. What is the domain and range of
y  x 4?
Part II: Composition of Functions
Use the functions below to answer #12-15.
f ( x)  x 2  2 x  4
g ( x)  3x  4
12.  f g  (2)
13.  h g  (3)
14. g ( f ( x))
15. f ( g ( x))
h( x )  4 x  3
Part III: Inverse Functions
#16-17, find the inverse of each function and state whether the inverse is a function or not.
16. f ( x) 
1
x4
2
17. g ( x)  ( x  4)2