In Class Exam 1 Review

 

1. Find the domain of each function.

 

a)       

 

 

 

  b)     

 

 

 

 

 

 

  c)    

 

 

 

 

 

 

 

 

 

 

  d)     

 

 

 

 

 

 

 

e)

 

 

 

 

 

 

 

2. A producer of an electronic game finds that at $50 or higher they can sell none. For each decrease of $5 in the price they can sell 1000 more games. Their fixed costs are $20,000 and total cost for 1000  games is $45,000. Assume demand and cost are linear. Find the quantity they should produce for maximum profit, the maximum profit and the break even points.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3. A tax is 5% of income if income is $20,000 or less. For income above $20,000, the tax is $1000 plus 10% of any income above $20,000. Express the tax as a piecewise function of income. Graph this function.

 

 

 

 

 

 

 

 

 

 

 

 

 

4. Find the difference quotient at (3, f(3)) for .

 

 

 

 

 

 

 

 

5. Graph the piecewise function

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6. For a and b write in vertex form and give the transformations of y= which result in f(x). Give the vertex, axis, range, x intercepts and y intercept of f.

a)     

 

 

 

 

 

 

 

 

 

 

 b) 

 

 

 

 

 

 

 

 

c) What transformations of y=lnx result in f(x) = 3ln(x+2) + 7

 

 

7. Find the asymptotes of each function.

 

a)         

 

 

 

 

 

 

  b)       

 

 

 

 

 

c)

 

 

 

 

8. Find all solutions for x.

 

a) 2log x + log 5 = 2 

 

 

 

  b)     

 

 

 

 c)    

 

 

d)   

 

 

e)   

 

9. $3000 is invested at annual interest rate 9%. Find the amount after t years, the doubling time and the time to reach $4500 if interest is compounded

 

a) semiannually    

 

 

 

 

 

 

 b) continuously

 

 

 

 

 

 

 

 

 

 

10. A person anticipates a need for $60,000 twelve years from now. How much should he invest (present value) if interest is

 

a)  5% compounded monthly?    

 

 

 

 

 

b) 5% compounded continuously?

 

 

 

 

c) If he has $25000 to invest today, what interest rate must he earn?

 

 

 

 

 

 

 

 

 

 

  1. Compute the limit or state it does not exist. 

.a)

 

 

 

 

 

 

 

b)    for   

 

 

 

c)

 

 

  1. Where is the function not continuous?

a)

 

 

 

 

 

 

 

 

 

 

 

b)

 

 

 

Given a graph of a function, be able to find left and right hand limits at given x-values. Be able to determine where the limit does not exist and where the function is not continuous.

 

  1. Find each limit. The answer should be a number, + or -.

 

a)                   b)

 

 

  1. Each set of data perfectly fits a function type which we studied. View the data in a plot and determine which type of function it would be. Then find a regression model for which

 

a)   x          -3          -1         3        5

      y        0.85      -1.05    2.35   7.65

 

b)   x         -2       0       1       2        3       4      5

      y           5      -1      3.5    9     12.5    11    1.5

 

c)   x       -3        -2         -1        0      1      2

      y    .375       .75         1.5     3       6    12