MATH QUIZ 6

1.      Determine whether each of the following graphs represents a one-to-one

function.

 

(a)

 

    

         (b)

   

 

 

 

 

 

 

 

(c)  

 

 

 

(d)

 

 

 

 

 

 

 

2.       For each part below, determine if an inverse for the given f( x )

          exists.   If an inverse exists, then please find the inverse.  

         Otherwise, write “NO INVERSE”.      

 

(a)            f( x ) = 3x + 3

 

 

 

 

 

 

 

(b)    

 

 

 

 

 

 

 

 

 

 

(c)      f( x ) =  7

 

 

 

 

 

 

 

(d)     f( x ) = 5x²  +  4x

 

 

 

 

 

 3.    In order to check to make sure we have the right inverse for a

       given f( x ), we can check that  and also that

       .    Using that idea of checking, please check to 　　

　　 make sure that the inverse you got in #2 (a) is the correct inverse

        for f( x ) = 3x + 3.

 

 

 

4.  The following formula can be used to convert Fahrenheit temperatures

     x to Celsius temperatures T(x):

                   

a)     Find T(-13)  and  T(86).

 

 

b)     Find T^-1(x) and explain what it represents.

 

 

 

 

5.   Please choose which equation represents the following graph:

 

A.    f( x ) = -e^x

B.    f( x ) = -e^x + 1

C.    f( x ) = e^-x + 1

D.    f( x ) = e^x – 1

 

6.  Please choose which equation represents the following graph:

 

A.    f( x ) = 2^{x – 1}

B.    f( x ) = 2^x – 1

C.    f( x ) = -2^{x – 1}

D.    f( x ) = -2^x – 1

7.  Water initially at 130 degrees Fahrenheit is left in a room of temperature

     70 degrees Fahrenheit to cool.   After t minutes, the temperature T of the

water is given by

                     

Find the temperature of the water 10 minutes after it is left to cool.

 

 

 

 

8.        Suppose that $100,000 is invested at 4% interest, compounded

 monthly.  Find the amount of money in the account after 10 years.

 

 

                   

 

 

9.  Find each of the following, and round answer to the nearest 4 decimal places.

 

(a)    e⁴

 

 

(b)   e^-2

 

 

(c)    log  50

 

 

(d)  log₂ 128

 

 

(e)    ln 50

 

 

10.   Find log₄ 50 using the change of base formula, and round answer to the

        nearest 4 decimal places.

 

 

 

 

11.  Students in an accounting class took a final exam and then took equivalent

       forms of the exam at monthly intervals thereafter.   The average score

       S(t), as a percent, after t months was found to be given by the function

            S(t) = 78 – 15 log(t + 1)

 

 

(a)   What was the average score when the students initially took the

test?

 

 

 

 

(b) What was the average score after 4 months?   after 24 months?

 

 

 

12.   Express  log 2x as a sum of logarithms.

 

 

13.  Express    as a product.

 

 

14.  Express      as a difference of logarithms.

 

 

FOR  #15  AND #16,  EXPRESS IN TERMS OF SUMS AND DIFFERENCES

OF LOGARITHMS.

 

15 

 

 

16. 

 

 

FOR  #17  AND #18,  EXPRESS AS A SINGLE LOGARITHM, AND IF POSSIBLE, SIMPLIFY.

 

17.   ln 44 – ln 4

 

 

18.   

 

 

FOR #19 AND #20, LET  ,  , AND , FIND EACH OF THE FOLLOWING:

 

19. 

 

 

20.