7.6 Variation

Let kbe a real number.

If then yvaries directly as

If then yvaries inversely as

If ykxz, then yvaries jointly as xand z.

y xn.

k

xn

,

ykxn, xn. The area of a circle varies directly asthe square of the radius.

Here,

Pressure varies inversely asvolume.

For a given principal, interest varies jointly asinterest rate and time.

I=krt kis the given principal.

p=

k

V

a=kr^2 k=p.

CONCEPTS EXAMPLES

REVIEW EXERCISES

CHAPTER 7

7.1 (a)Find all real numbers that are excluded from the domain. (b)Give the domain,

using set-builder notation.

1. 
   
   
   
   2. 3.ƒ 1 x 2 =
   
   
   
   

9

x^2 - 18 x+ 81

ƒ 1 x 2 =

5 x+ 17

x^2 - 7 x+ 10

ƒ 1 x 2 =

- 7

3 x+ 18

Write in lowest terms.

4. 
   
   
   
   5. 
      
      
      
      6. 
         
      
      
      
      
   
   
   
   

7.What is meant by the reciprocal of a rational expression?

Multiply or divide. Write the answer in lowest terms.

8. 
   
   
   
   9. 
      
   
   
   
   

10. 11.

7.2 Suppose that each expression is the denominator oƒ a rational expression. Find the

least common denominator for each group.

12. 
    
    
    
    13. 
        
    
    
    
    


13. 
    
    
    
    15. 
        
    
    
    
    

Add or subtract as indicated.

16. 
    
    
    
    17. 
        
    
    
    
    

18. 19.

20.Concept Check Two students worked the following problem. One student got a sum of

and the other got a sum of Which student(s) got the correct answer?

2

y-x

+

1

x-y

• 1
  x-y.

1

y-x

3 r

10 r^2 - 3 rs-s^2

+

2 r

2 r^2 +rs-s^2

6

5 a+ 10

+

7

6 a+ 12

5 y+ 13

y+ 1

-

1 - 7 y

y+ 1

5

3 x^6 y^5

-

8

9 x^4 y^7

6 x^2 + 13 x-5, 9 x^2 + 9 x- 4 3 x-12, x^2 - 2 x-8, x^2 - 8 x+ 16

32 b^3 , 24 b^59 r^2 , 3 r+1, 9

m^3 - n^3

m^2 - n^2

,

m^2 +mn+n^2

m+n

z^2 - z- 6

z- 6

z

(^2) - 6 z
z^2 + 2 z- 15
w 2 - 16
w
#^3
4 - w
12 y+ 322
5 y
#^15 y
3
4 y^2 - 9
r- 2
4 - r^2
25 m^2 - n^2
25 m^2 - 10 mn+n^2
12 x^2 + 6 x
24 x+ 12

420 CHAPTER 7 Rational Expressions and Functions