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18002014091
MAT 1800 FINAL EXAM
Read the directions to each problem carefully. ALL WORK MUST BE SHOWN IN THE PROVIDED
BLUE BOOK. Only minimal credit will be awarded for answers without supporting work. Each problem is
worth 10 points. DO NOT USE A CALCULATOR.
1. Solve 8  2 x  1  6 . State your answer in interval notation.
2. Let f x    x 2  3x  5 and g x   2 x  1 . Find and simplify each of the following.
(a)
g  f 2
 f  g 0
 x2

3. Sketch a graph of the function g x    x  1
 5

4. Find the domain of the function f x  
(b)
 f  f x
if
x  1
if
1  x  3
if
x3
ln 3  5 x 
. State your answer in interval notation.
1 x 1
5. Let f x   3  x . Find the average rate of change of f x  from x  a to x  a  h and
simplify your answer so that no single factor of h is left in the denominator.
6. Graph the polynomial px    x 3 x  4x  22 , finding and labeling all intercepts.
7. Find all zeros of the polynomial Px   x 3  2 x 2  3x  10 . Please express any non-real zeros in
the form a  bi .
8. The circumference of a circle is x inches. Find a function of x that models the area of the
circle. Simplify your answer.
9. Graph the function f x  
7x  x2
, labeling all intercepts and asymptotes.
x 2  4x  4
10. Graph the function f x   2  e 5 x , labeling any asymptotes and at least one point.
11. Find the exact value of each expression.
(a) log 81 3
(b) 4 log
16
7 
12. Solve the logarithmic equation log11 x  1  log11 x  1  log11 x  5 .
13. Let f x   87 x4  8 . Find f 1 11 , where f 1 is the inverse function of f .
14. The general function Pt   P0 e rt is used to model a dying fish population, where n0 is the
initial population and t is time measured in years. Suppose the population initially contains
700 fish and after 6 years there are only 28 fish remaining. How long did it take for the fish
population to decline to one-fifth its initial size? Simplify your answer completely.
15. Find the exact value of each trigonometric function at the given real number, if it exists.
17 

 6 
(a) tan
9 

 4 
(b) csc 
16. Find the exact value of each expression, if it exists.

7 
(a) cos 1  sin  
  6 

 2 
 
1
(b) tan sin   
7

5
with  in Quadrant IV and tan   2 with  in Quadrant III, find the
6
exact value of cos    .
17. Given that sin   
18. State the amplitude and period length of the function g x   3 cosx  2  and then graph one
complete period. Be sure to label the highest and lowest points on the graph.
19. Verify that the trigonometric equation is an identity.
cos2 x   sin x   1
  tanx 
cosx   sin 2 x 
20. Find all primary solutions (i.e. 0  x  2 ) of the equation 3 tanx cos 2 x   tanx sin 2 x  .