Math 1150: Precalculus, Instructor: Dana Ernst

Solutions to Review for Midterm Exam  #2

 

Here are the solutions to the review.

 

1. (a)
   
     (b)
   
     (c)
   
     (d)
   
     (e)  
   

 

2. (a) All reals  (b)  No solution  (c)
   
     (d)
   
   , note that the second interval has parentheses instead of brackets because those values are not in the domain of the corresponding function.

 

3. The graph is the graph of
   
    reflected down, stretched vertically by a factor of 2, shifted right 2, and up 1.

 

4.  
   

 

5.  
   

 

6.  
   

 

7. See Book

 

8. See Book

 

9. n

 

10. Yes, but one of the roots has to have multiplicity 2.  For example,
    
     has 5 distinct real roots and 1 has multiplicity 2 (for a total of 6 linear factors).

 

11. No, complex non-real roots always come in conjugate pairs, and so there will always be an even number of them.  Hence there can’t be 3 of them.  Note that my wording was a bit ambiguous since I didn’t explicitly say “3 complex non-real roots.” 

 

12.  
    

 

13. 0, -1, 4

 

14. Many possible answers, but the most likely is
    
    .

 

15. The graph has x-intercepts at
    
     and
    
    .  The first of these has multiplicity 2, and so graph bounces off x-axis at
    
    .  The other has multiplicity 1, and so graph crosses at
    
    .

 

16.  
    

 

17. Only 1 is a root.

 

18. 
    
     is a factor of a polynomial if and only if h is a zero of the polynomial.

 

19.  
    

 

20.  
    

 

21. 0, -3, -4

 

22.  
    

 

23.  
    

 

24. Other zeros are:  
    

 

25.  
    

 

26. Vertical asymptote:
    
    , Horizontal asymptote:  
    

 

27. I’ll do these for you in class.

 

28. See Book