Bergen Community College Intercepts and Asymptotes Precalculus Final Exam

Handwrite answers on pieces of papers, and take picture of them, I really need to get a hundred, please check your answers, after you do them.

Precalculus
Final Exam
Prof. Ockay
Directions: Do all work and put all answers on the blank sheets,
NOT on the test. Use correct notation, state any formulas used, and
show your work.
1. Sketch a reasonable graph of        (7 points)
2. Solve the equation: 6   (round the answer to 4 decimal
places. (5 points)

3. Graph   
. Clearly label all intercepts and asymptotes.
(8 points)
4. Write as a sum, difference, or product of logarithms: (5 points)
log 
 


5. Graph each function clearly label the intercepts and
asymptotes: (3 points each)
a)   
b)   ln   
6. Find the exact value of cos , if tan   
(6 points)

3
and sin   .
7. Graph one period of the function    cos 3    . Include
all intercepts. Label the  values for which the function has its
maximum or minimum values. (8 points)
8. Simplify: cos 

 
 sin  
(7 points)
cos 
9. Verify the identity: cos  
sin 

sin 
cos     (8 points)
10. Find all solutions of the equation in the interval [  :
(give the answer in radians)
sin   
(8 points)

11. Given sin   
, with      , find the exact value of
cos  and sin  using the double angle identities.
(8 points)
12. Give the exact value of tan (arcsin     ). (8 points)
13. Rewrite the expression so that it is not in fractional form:
tan 
csc   cot 
14. Let       find and simplify
(8 points)
(8 points)
  

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