AP Calculus
Unit 1: Limits and Their Properties
Lab Assignment #1
This assignment is due on or before Wednesday, September 15, 2010. This
part of the assignment is worth 30 points. Note: You may use a graphing
calculator to check your work, but you must work out all parts of the
assignment manually for full credit. All final answers must be in sentence
form. Answers of “I used the graphing calculator” will not be accepted.
x2  2 x  1
Given the function f ( x )  2
, 5  x  5
x  3x  4
a) State the domain of the function.(2 pts)
b) State the range of the function.(3 pts)
c) Determine if the function is even, odd, or neither. Show your work
and explain your reasoning.(3 pts)
d) Describe the symmetry, if any, of the graph. Explain your
reasoning.(3 pts)
e) Find the zero(es) of the function. Show your work.(3 pts)
f)
Determine if the function has any discontinuities on the interval
5  x  5 and state whether the discontinuity(s) is/are removable or
nonremovable. Justify your reasoning.(3 pts)
g) Determine the vertical asymptotes, if any, and write the equation
for each.(3 pts)
h) Use the information in parts a-g to sketch the graph of the function.
Be sure to label your axes.(5 pts)
i)
Is the function continuous at x  0 ? Use the definition of continuity
to prove your answer.(5 pts)