advanced algebra d name key 4. =4 -...

Advanced Algebra D Name Key

9.1 Worksheet – Variation Date Block

State whether each equation represents a direct, joint, or inverse variation. Then name the constant of variation.

1. � = 8�� 2. � = 4� 3. =

� 4. � = 4.5

Joint, 8 direct, 4 inverse, 5 inverse, 4.5

5. �

�= � 6. 2� = �� 7.

�.�

�= ℎ 8. =

�

��

Direct, π joint, ½ inverse, 1.25 inverse, ¾

Find each value.

9. If varies directly as � and = 8 when

� = 2, find when � = 6.

= �

8 = !2"

4 =

= 4�

= 4!6"

= 24

10. If varies directly as � and = −16 when

� = 6, find � when = −4.

= �

−16 = !6"

−8

3=

= −8

3�

−4 = −8

3�

3

2= �

11. If & varies directly as ' and & = 132 when

' = 11, find & when ' = 33.

& = '

132 = !11"

12 =

& = 12'

& = 12!33"

& = 396

12. If varies jointly as � and � and = 24

when � = 3 and � = 1, find when

� = 12 and � = 2.

= ��

24 = !3"!1"

8 =

= 8��

= 8!12"!2"

= 192

13. If * varies jointly with � and the square of +

and * = 30 when � = 15 and + = 2. Find

� when * = 6 and + = 8.

* = �+�

30 = !15"!2"� 1

2=

* =1

2�+�

6 =1

2�!8"�

3

16= �

14. If * varies jointly as - and � and * = 60

when - = 3 and � = 4, find - when

* = 240 and � = 8.

* = -�

60 = !3"!4"

5 =

* = 5-�

240 = 5-!8"

6 = -

15. If varies inversely as � and = −18

when � = 2, find when � = 5.

=

�

−18 =

2

−36 =

=−36

�

=−36

5

16. If varies inversely with the square of �,

and = 50 when � = 4. Find � when

= 32.

=

��

50 =

!4"�

800 =

=800

��

32 =800

��

�� = 25

� = ±5

17. If + varies inversely as / and + = 3 when / = 5, find / when + = 2.5.

+ =

/

3 =

5

15 =

+ =15

/

2.5 =15

/

/ =15

2.5

/ = 6

18. If & varies directly with � and inversely with the square of ', and � = 48 when & = 8 and ' = 3. Find �

when & = 12 and ' = 5.

& = �

'�

8 = !48"

!3"�

3

2=

& =3�

2'�

12 =3�

2!5"�

200 = �

19. The volume 0 of a gas varies inversely as its pressure 1. If 0 = 80 cubic centimeters when 1 = 2000

millimeters of mercury, find 0 when 1 = 320 millimeters of mercury.

0 =

1

80234 =

20005�33

160,000234∙5�33 =

0 =160,000234∙5�33

1

0 =160,000234∙5�33

3205�33

0 = 500234

20. The length 7 that a spring will stretch varies directly with the weight 8 that is attached to the spring. If a

spring stretches 20 inches with 25 pounds attached, how far will it stretch with 15 pounds attached?

7 = 8

209: = !25;<=" 49:

5;<==

7 =49:

5;<=8

7 =49:

5;<=!15;<="

7 = 129:

21. The area > of a trapezoid varies jointly as its height and the sum of its bases. If the area is 480 square

meters when the height is 20 meters and the bases are 28 meters and 20 meters, what is the area of a

trapezoid when its height is 8 meters and its bases are 10 meters and 15 meters?

> = ℎ!-� + -�"

4803@ = !203"!283 + 203"

4803@ = 960 3@ 1

2=

> =1

2ℎ!-� + -�"

> =1

2!83"!103 + 153"

> = 1003@

22. Describe the combined variation modeled by the formula =A!="@B

��. Be sure to state the type of

variation(s), the variables used in the variation(s), and the constant of variation.

varies jointly with the square of � and ℎ and inversely with �. The constant of variation is A

�.

Advanced Algebra D Name

9.2 Worksheet – Reciprocal Function Date Block

Write an equation for a translation of = −�

� that has the given asymptotes.

1. � = 2; = 1 2. � = −1; = 3 3. � = 4; = −2

= −�

�D�+ 1 = −

�

�E�+ 3 = −

�

�D�− 2

4. � = 0; = 6 5. � = 3; = 0

= −�

�+ 6 = −

�

�D�

Sketch the asymptotes and the graph of each function. State the domain, range, asymptotes, and limits.

6. F!�" =�

� 7. F!�" =

�

�D�

D: !−∞, 0"⋃!0,∞" R: !−∞, 0"⋃!0,∞" D: !−∞, 1"⋃!1,∞" R: !−∞, 0"⋃!0,∞"

Hor Asy: = 0 Ver Asy: � = 0 Hor Asy: = 0 Ver Asy: � = 1

limL→EN

F!�" = 0 lim�→DN

F!�" = 0 limL→EN

F!�" = 0 lim�→DN

F!�" = 0

lim�→OD

F!�" = −∞ lim�→OE

F!�" = ∞ lim�→OD

F!�" = −∞ lim�→OE

F!�" = ∞

8. F!�" = −�

�D�− 3 9. F!�" =

�

�+ 3

D: !−∞, 2"⋃!2,∞" R: !−∞,−3"⋃!−3,∞" D: !−∞, 0"⋃!0,∞" R: !−∞, 3"⋃!3,∞"

Hor Asy: = −3 Ver Asy: � = 2 Hor Asy: = 3 Ver Asy: � = 0

limL→EN

F!�" = −3 lim�→DN

F!�" = −3 limL→EN

F!�" = 3 lim�→DN

F!�" = 3

lim�→�D

F!�" = ∞ lim�→�E

F!�" = −∞ lim�→OD

F!�" = −∞ lim�→OE

F!�" = ∞