ANSWER SHEET – RATIONAL FUNCTIONS MATCH GAME Names:_____________________________ Block:_____ Date:___________ NO CALCULATORS! Work in groups of 3 or 4. Match each of the 8 equation cards to the corresponding table, graph, and verbal description cards. Do NOT use your calculators! Record your answers in the table below. Show your work for simplifying the equations where indicated below and on the back. Simplifying is necessary in order to recognize important features of the functions. Complete the miscellaneous questions below, as well.

Equation Table Graph Verbal description

1

2

3

4

5

6

7

8

The following numbers correspond to the equation card numbers.

1) Simplify: (Hint: Factor out a negative 1 from the denominator first.)

2) Simplify:

Identify all “holes.” 3) Simplify:

Identify all vertical asymptotes: over

4) Simplify. Factor the quotient to find expressions for the length and width. Use this

information to complete the table.

5) Simplify:

6) Simplify:

Find the x- and y-intercepts, if they exist.

7) Divide to find oblique (end behavior) asymptote:

8) What type of variation is this? If you were driving an average speed of 60 mph, how many hours would it take to reach Wyoming? What would be the effect of increasing your average speed to 70 mph?

   

Ht. x

Area y

Length

Width Vol.

1 2 3 4

 

 

   

   

 

 

 

 

 

 

 

 

 

 

 

                                 

22

19

 

18

21

24

23

20

17

 

     

13

16

15

9

11

12

10

14

 

 

 

 

 

   

 

     

1

3

5

7

2

4

6

8

 

2    

 

 

 

   

 

   

     

26

30

27

32

28

25

31

29

As from the left, . As from the right, . As from either side, .

This graph has no x-intercept and no y-intercept.

This graph is decreasing over its entire domain.  

This function could be used to find the area of the rectangular base of a box of height x.

This function has vertical asymptotes at and . It has a horizontal asymptote at

.

This function has an x-intercept of .

It has a horizontal asymptote of .

This graph has no horizontal asymptote.

as .  

y could represent the time (in hours) that it takes to reach Wyoming as a function of how fast one is driving, x, in mph.  

ANSWER SHEET – RATIONAL FUNCTIONS MATCH GAME– ANSWER KEY Names:_____________________________ Block:_____ Date:___________ NO CALCULATORS! Work in groups of 3 or 4. Match each of the 8 equation cards to the corresponding table, graph, and verbal description cards. Do NOT use your calculators! Record your answers in the table below. Show your work for simplifying the equations where indicated below and on the back. Simplifying is necessary in order to recognize important features of the functions. Complete the miscellaneous questions below, as well.

Equation Table Graph Verbal description

1 13 22 26

2 11 24 28

3 16 19 30

4 12 17 25

5 15 18 27

6 10 23 31

7 9 21 32

8 14 20 29

The following numbers correspond to the equation card numbers.

1) Simplify: (Hint: Factor out a negative 1 from the denominator first.)

!x +8( )x + 5

or !x !8x + 5

2) Simplify:

4!

Identify all “holes.” x = !6,0,3

3) Simplify:

x +3

x ! 2( ) x + 5( ) Identify all vertical asymptotes: x = !5, x = 2 over

4) Simplify. Factor the quotient to find expressions for the length and width. Use this

information to complete the table.

5) Simplify:

11x + 406(x + 4)(x ! 4)

6) Simplify:

4x + 23x ! 2

Find the x- and y-intercepts, if they exist.

x = ! 12

but no y-intercept (There is a hole at x=0)

7) Divide to find oblique (end behavior) asymptote:

y = 2x +15

8) What type of variation is this? Inverse Variation If you were driving an average speed of 60 mph, how many hours would it take to reach Wyoming? 35 hours What would be the effect of increasing your average speed to 70 mph? It would decrease travel time to 30 hours.

 

Ht. x

Area y

Length

Width

Vol.

1 21 7 3 21 2 50 10 5 100 3 91 13 7 273 4 144 16 9 576