Honors AP Calculus / Mr. Hansen 9/13/2002 (optional re-do due 9/19/2002)

Name: _________________________ Quiz #3

Quiz (15 pts.) on §§1-1 through 1-3 and Class Content

** For 5 out of 5 points on the optional re-do, record your start time ______ and end time _____ , and be sure to do the bonus question. Practice working for speed as well as accuracy. **

1.	Use your calculator to transcribe a rough sketch of the function y = f (x) that is defined piecewise as follows: f (x) = –2x^2 + 14x – 7.1, if x < 3 [note correction by A. Hartz] f (x) = 25.85 – 3x, if x > 3 “Rough sketch” means just that. Show crossings and features only. Tick marks can be minimal. Use a domain that includes most or all of the interval [–2, 10].
2.	In #1, on the same set of axes, sketch the derivative of f and label it.
3.	On a separate set of axes, sketch a function g whose derivative could be f. In other words, find g such that g’(x) = f(x) on as much of [–2, 10] as possible.
4.	Can a function have a limit at a point even though the function is not defined there? Explain briefly (approx. one sentence, or a clear example).
Bonus (required for re-do)	Give a rigorous definition, including notation, of the left-handed limit of a function at a point.