Math worksheet

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) 3 2

( ) 2 5f x x x   

a) ( 2)f  b) (3)f c) (1 )f x

4) , 2

( ) 2, 2

x x g x

x x

    

  

a) (5)g c) ( 6)g  c) ( 2)g 

Problems 5-8. Is 𝒚 a function of 𝒙?

5) 2 3 7x y  6) 2

4x y  7) 2y x  8) 2

5x y 

Problems 9-14. Find domain, write in interval notation.

9)

2 4

( ) 22

x f x

  10)

3

2

2 ( )

9

x f x

x

 

 11)

2

2 ( )

7 12

x f x

x x

  

 

12) 2

( ) 3

x f x

x

 

 13)

2 , 2 ( )

5, 2

x x f x

x

   

 14)

5 ( )

( 2)( 25)

x f x

x x x

 

 

Problems 15-18. Graph.

15) 3, 4

( ) 2, 4

x f x

x

  

  16)

3 , 2

( ) 1 1, 2

2

x x

g x x x

   

      

17)

3, 3

( ) 2, 3 2

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

     

     

 

Problems 19-22. Determine if the function is even, odd, or neither. Show work.

19) 2

( )f x x x  20) 3 1

( )f x x x

  

21) 4 2

( ) 4f x x x  22) 5 3

( ) 1f x x x  

Problems 23-26. A function is given. Determine the average rate of change of the function between

the given values of the variable.

23) ( ) 3 8; 1, 4f x x x x     24) 2

( ) 2 ; 2, 4h t t t t t    

25) 1

( ) ; 2, 3 1

g x x x x

   

26) 2

( ) ; 0, 3

f x x x h x

   

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

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? ________________

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?

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.

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