Intermediate Algebra (11th edition)

SECTION 11.3 The Hyperbola and Functions Defined by Radicals 655

Complete solution available
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11.3 EXERCISES

Concept Check Based on the discussions of ellipses in the previous section and of hyperbo-

las in this section, match each equation with its graph.

1. A. B.

2.

3. C. D.

4.

Graph each hyperbola. See Examples 1 and 2.

5. 
   
   
   
   6. 
      
      
      
      7. 
         
      
      
      
      
   
   
   
   

8. 9. 10.

11. 12.

Identify the graph of each equation as a parabola, circle, ellipse,or hyperbola,and then sketch

the graph. See Example 3.

13. 
    
    
    
    14. 
        
        
        
        15. 
            
        
        
        
        
    
    
    
    


14. 
    
    
    
    17. 
        
        
        
        18. 
            
        
        
        
        
    
    
    
    


15. 
    
    
    
    20. 
        
        
        
        21. 
            
        
        
        
        
    
    
    
    

22.State in your own words the major difference between the definitions of ellipseand

hyperbola.

Graph each generalized square root function. Give the domain and range. See Examples 4

and 5.

23. 
    
    
    
    24. 
        
        
        
        25. 
            
        
        
        
        
    
    
    
    

26. 27. 28.

29. 30.

y

2

=

B

1 +

x^2

4

y

3

=

B

1 +

x^2

9

y=- 3

B

1 -

x^2

25

y=- 2

B

1 -

x^2

9

ƒ 1 x 2 =- 225 - x^2

ƒ 1 x 2 = 216 - x^2 ƒ 1 x 2 = 29 - x^2 ƒ 1 x 2 =- 236 - x^2

x^2 - 2 y= 0 x^2 + 9 y^2 = 9 y^2 = 4 +x^2

9 x^2 = 144 + 16 y^2 y^2 = 36 - x^29 x^2 + 25 y^2 = 225

x^2 - y^2 = 16 x^2 +y^2 = 16 4 x^2 +y^2 = 16

y^2

9

-

x^2

9

= 1

y^2

16

-

x^2

16

= 1

x^2

49

-

y^2

16

= 1

x^2

25

-

y^2

36

= 1

y^2

9

-

x^2

4

= 1

y^2

4

-

x^2

25

= 1

x^2

25

-

y^2

9

= 1

x^2

16

-

y^2

9

= 1

x^2

25

-

y^2

9

= 1

x^2

9

-

y^2

25

= 1

x^2

9

+

y^2

25

= 1

x^2

25

+

y^2

9

= 1

x

y

0

–3

–5 5

3

x

y

0

3

–3

• 55

x

y

–3 3

0

–5

5

x

y

0

–5

5

–3 3