Math 131 In-Class Exam 1 Review

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

2. A copier company charges 25 cents per page for the first 100 pages plus 20 cents per page for the remaining pages. Write the charge as a piecewise function of the number of pages, x.

3. f(x) is a transformation of . The vertex is at (3, 10) and f(2)=15. Without using an x-distortion, write the formula for f(x).

4. Find the formula for the function:

5. Find functions f and g so that: a) . b) .

6. A culture starts with 200 cells and increases by 50% every 3 hours.

a) Find N(t), the number of cells after t hours.

b) Write N(t) in base e.

7. The table shows the price of a U.S. postage stamp in cents for different years.

year 1919 1932 1958 1963 1968 1974 1978 1985 1991 2009

year-1919 0 13 39 44 49 55 59 66 72 90

price 2 3 4 5 6 10 15 22 29 42

Let x be the number of years past 1919.

Do quartic regression and exponential regression. Which is a better fit to the given data?

Which looks better for future data?

8. Find the inverse function to: a) . b) .

9. Solve for x:

10. Find the average velocity between t=2 and t=5 seconds for , where d(t) is the distance traveled along a straight line in feet per second. Find the instantaneous velocity at t=2 secs.

11. Evaluate each limit or write DNE if it does not exist.

12. Evaluate each limit as a number, as plus infinity, minus infinity, or write DNE.

13. Find the discontinuities of each function and give a reason for each discontinuity, either graphical or from the definition of continuity.

a) b)