1. [25 points]  Fill in the following table.  For the “Type” column, enter the letter according to the following list which best represents the type of function f(x) is.

 

            A. Linear          B. Quadratic                 C. Polynomial (other than A or B)

D. Rational       E. Exponential              F. Power          G. Logarithmic 

H. None of these

 

For the two columns at the far right, use g(x) = -2x

 

f(x)

Type

Domain

of f(x)

f(x + h)

  (Don’t need to simplify)

f(g(x))

(Simply your result)

g(f(16))   (Give an exact answer)

 

 

 

 

 

-3 log4 (-2x)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.  When a bicycle shop sells x racing bikes in a month, the revenue is –3x2 + 1800x, in dollars.  The shop’s fixed costs per month total $72,000, and each bike costs the shop $420.

 

a)      [5 points]  Write a function for the shop’s monthly costs, C(x):

 

 

 

 

 

b)      [5 points]  Write a function for the shop’s monthly profit, P(x):

 

 

 

 

 

c)      [5 points]  Find the quantity(s) of bicycles sold for which the shop breaks even.  Write one or two sentences to explain your methods.

 

 

 

 

 

 

 

 

 

 

d)      [5 points]  How many bicycles must be sold to maximize profit?  What is the maximum profit?  Explain your methods.

 

 

 

 

 

 

 

 

 

 

3.  [5 points]  Suppose the graph of f(x) = log x is shifted 5 units to the right, stretched vertically by a factor of 4, reflected over the x-axis, and then shifted down 2 units.  Write a new function that would define the graph resulting from this transformation.

4.  [5pts]  Solve the following equation for x:

 

 

 

 

 

 

 

 

 

 

5.  [10pts.]  Circle the letters of the items that represent functions:

 

a)                                                      b)                                     c)                   

                       

 

 

 

 

d)                                                                     e)

 

 

 

 

 

 

 

6.   [10pts]  How long does it take for $1000 to grow to $2500 in an account earning 8.5% interest compounded quarterly?

7. [20pts]  The following table gives the number of households, in thousands, connected to the Web during a given year, in Bedrock.

 

Year

1990

1992

1994

1996

1998

2000
Number

.56

1.11

2.20

4.32

8.52

15.80

(Note: Let x = 0 correspond with 1990).

a)      [6 points] Find the following best-fit models for this data.  Round all coefficients to the nearest hundredth.

 

Quadratic model:

 

 

Exponential model: 

 

 

Logistic model:

 

 

b)       [4 points] Comparing ONLY the quadratic and exponential models, which model is better?  Give mathematical justification.

 

 

 

 

 

 

 

 

c)  [4 points]  If the number of households in Bedrock will stay about the same over time, which of the three models is the best choice?  (There is a correct answer!)  Explain your answer.

 

 

 

 

 

 

 

 

d)  [3 points] Using the model you chose in part c), estimate the number of households in Bedrock that will be connected to the Web the year 2010.

 

 

 

 

e)       [3 points] Estimate the year in which 50,000 people will be connected to the Web in Bedrock.

8.       [5 points]  If the graph below shows q(x), sketch the graph of 2q(-x) + 1.