MTH 106; fall 2005
Test: Chapters 1 & 2
All questions in section I are worth 3 points each. All other questions are worth 6 points each.
I.
The graph of g(x) is given below. Answer the following questions about g(x).
1. Is g(x) a function?_______ How do you know?
2. State the domain of g.
3. State the range of g.
4. State the value(s) of x for which g(x) = 0.
5. lim g ( x) 
x  -8
6.
lim - g ( x) 
x  -2
7. lim g ( x ) 
x 5
8.
lim g ( x) 
x  -
9. lim g ( x) 
x 
10. State the equations of all asymptotes of g.
11. g(g(2)) =
12. For what value(s) of x is g(x) discontinuous?
13. Is g(x) continuous from the right, left, or neither at x = -2?
14. What part of the definition of continuity fails at x = 2?
15. For what value(s) of x does g(x) have a removable discontinuity?
II.
Given that h(x) = x  1 and k(x) = x4 + x2 , a) find k ◦ h ,
III.
Is p(x) = 5x4 – 3x2 + 1 an even, odd, or neither even nor odd function? Show your work used for
checking.
b) simplify, and c) state the domain.
IV.
Find the following limits; show any necessary work.
x 2  5x
A. lim 2

x  5 x  x  20
B. limx 3
1 x

x3
sin 3 (5 x)
C. lim 3

x  0 x cos( 7 x )
5x 3  7 x 2  4

x - 
2x 4  3
D. lim
E. lim
x - 
25x 2  5x

6x  1
F. What does your answer to D above tell you about asymptotes for the given function?
V.
The function a(x) is shown below. For what value(s) of x is a(x) discontinuous? _______________
For each of those values of x, tell why a(x) is discontinuous there. Show your work.
a(x) =
x2 – 2 if x ≤ -1
1
if -1 < x < 2
x
x + 4 if x ≥ 2