Math 131 Exam 1 Review

1. Find the domain of each function, f(x)=

2. A tax schedule requires you to pay 15% of the first $20000 of income plus 20% of the

amount above $20000. For example a person earning $50000 pays 15% of $20000 plus 20% of $30000. Write the tax as a piecewise function of income, x.

3. f(x) is a transformation of . The range of f is , f(-3)=12 and f(0)=-6.

You do not need a horizontal distortion. Write a formula for f(x).

4. f(x) is a transformation of y=ln(x). f(x) approaches minus infinity as x approaches 2, f(3)=7 and f(e+2)=10. Write a formula for f(x) assuming no x-distortion was done.

5. 9. Solve for A, B and C if

6. A culture begins with 100 cells and grows exponentially so that after 2 hours, there are 250 cells. Find N(t), the number of cells after t hours.

7. Give two possibilities for f and g if .

8. An account earning continuous compound interest had the values shown at ends of the first through the fifth years.

year, x 1 2 3 4 5

account

value 1056.54 1116.28 1179.40 1246.08 1316.58

a) Do an exponential regression and write the exponential model.

Write the model in base e using.

Estimate the annual interest rate and the initial principal.

b) According to the model, what is the approximate doubling time? tripling time?

c) If the y values in the table were replaced by lny, which model would best fit?

d) If the x and y values in the table were switched, which model would best fit?

9. Solve for x if:

10. Solve for x exactly without a calculator.

11. A particle travels in a straight line. The directed distance from a reference point is given by d(t) ft. where t is in seconds. Find the average velocity for t between 1 and 3 secs.. Find the instantaneous velocity at t=1 sec.

12. Evaluate each limit or state DNE if it does not exist.

13. Find the value of c which makes f(x) continuous for all x.

14.

Find a) .

Is f left continuous at 0, right continuous at 0, both or neither?

15. Find all discontinuities of f(x) and give either a graphical or a definition reason for each discontinuity.

16. Find each limit as a number, infinity or minus infinity, or state DNE.

f)