This document contains 31 problems related to functions, including evaluating functions, determining domains and ranges, determining if relations are functions, graphing functions, finding average rates of change, and analyzing features of graphs such as intercepts, local extrema, and intervals of increasing/decreasing behavior. Suggested additional practice problems are listed at the end from the textbook and unit worksheets to further reinforce these concepts.

1. Worksheet 4 Name:
Problems 1-2. Is the relation a function? Determine the
relation’s domain and range.
1) {(red, 3), (blue, 3), (green, 3)} 2) {(1,3), (2,4), (3, 5),
(2,6)}
Problems 3-4. Evaluate.
3)
4)
, 2
( )
2, 2
x x
g x
x x

2. Problems 5-8. Is � a function of �?
Problems 9-14. Find domain, write in interval notation.
9)
2 4
( )
22
x
f x
3
2
2
( )

3. 9
x
f x
x
11)
2
2
( )
7 12
x
f x
x x

4. 12)
2
( )
3
x
f x
x
13)
2 , 2
( )
5, 2
x x
f x
x
14)
5
( )

5. ( 2)( 25)
x
f x
x x x
Problems 15-18. Graph.
15)
3, 4
( )
2, 4
x
f x
x
16)

6. 3 , 2
( ) 1
1, 2
2
x x
g x
x x
17)
3, 3
( ) 2, 3 2

7. 3, 2
x x
h x x
x x
18)
3, 3
1
( ) 1, 3 3
3
2, 3
x x
f x x x
x x

8. Problems 19-22. Determine if the function is even, odd, or
neither. Show work.
19)
3 1( )f x x
x
21)

9. Problems 23-26. A function is given. Determine the average rate
of change of the function between
the given values of the variable.
24)
25)
1
( ) ; 2, 3
1
g x x x
x
26)
2
( ) ; 0,
3
f x x x h
x

10. 27) The following table shows the number of CD players sold in
a small electronics store in the years 1996-
2000. Use the table to answer the following questions.
a) What was the average rate of change of sales between 1996
and 2000?
b) What was the average rate of change of sales between 1998
and 1999?
c) Between which two successive years did CD player sales
increase most quickly?
Year CD Players Sold
1996 410
1997 468
1998 510
1999 590

11. 2000 607
28) Use the graph below to answer the following questions.
Function? ____________
Domain: ____________
Range: ____________
29) Use the graph below to answer the following questions.
Function? ________ F(-2)=__________
Domain: ________ Where is F increasing?
________________
Range: ________ Where is F decreasing?
________________

12. Are there any absolute extrema? If so, describe.
30) Use the graph below to answer the following questions.
Function? ___________ Domain: ___________ Range:
___________
f(-2)=_______________ f(4)=______________
f(2.46)=__________
Intercepts:
_____________________________________________________
________
Where is f increasing? ________________________
Where is f decreasing? ________________________
Local Maximum(s): __________________________
Local Minimum(s): ___________________________
Are there any absolute extrema? If so, describe.
For what values of x does f(x)=0?

13. 31) Use the graph below to answer the following questions.
Function? __________ f(0) = ____________
Domain: __________ Intercepts: ____________
Range: __________ ____________
For what values of x does f(x)=-1?
Where is f increasing? Use interval notation.
Where is f decreasing? Use interval notation.
Local minimums: ___________________
Local maximums: ___________________
Are there any absolute extrema? If so, describe.

14. If you feel that you need additional practice on this material
attempt the following book
problems or Unit 2 Additional Practice Worksheets:
(Book) Section 3.1: 9-37 (odd), 41-59 (odd)
(Book) Section 3.2: 7-45 (odd)
(Book) Section 3.3: 5-33 (odd)
(Unit Two Additional Practice WS) Average Rates of Change
(Unit Two Additional Practice WS) Continuity
(Unit Two Additional Practice WS) Extrema, Increase and
Decrease
(Unit Two Additional Practice WS) Piecewise Functions
(Unit Two Additional Practice WS) Evaluating Functions