Worksheet – Section 3.2
Name__________________________________
1. Give an example of a power function which is not a polynomial?
2. Give an example of a polynomial function which is not a power function.
3. What is the domain of any polynomial?
4. If x  a is a zero of a polynomial, what is one of its factors?
5. If the degree of a polynomial is odd, what is the least number of horizontal- intercepts?
Explain
6. If the degree of a polynomial is even, what is the least number of horizontal- intercepts?
Explain
7. For any polynomial what is the least and most vertical intercepts? Explain.
8. Match column A with all possible answers from column B.
Note: In some cases there may be more than one answer, answers may be used in more than
one expression and some answers may not be used.
Column A
Column B
x2 1
_________ i. 2
x 1
a. polynomial of degree 2
_________ ii. x 3  5
b. odd function (graphs are helpful)
_________ iii.  x  4   10
c. even function (graphs are helpful)
_________ iv. x 2  4
d. y -intercept is (0,6)
2
_________ v.
1
x
e. even degree polynomial
_________ vi. x 3  x  1
f. has no x -intercepts
_________ vii. x  4( x  6)
g. has exactly two zeros
h. odd degree polynomial
9. For each of the following
(i) write an equation for a 4th -degree polynomial with the condition given below (factor
form is best) (ii) Sketch its graph. If it can’t be done explain why.
(a) with four real zeros
(b) with two real zeros
(d) with three real zeros
(e) with 5 real zeros
(c) with 1 real zero
(f) with no real zeros