1147 MAC (4258) - Quiz #5
Name:
Key
For full credit, you must show all work and circle your nal answer.
1
Use long division OR synthetic division to divide. (1.5 points)
(9x3 16x 18x2 + 32) (x 2)
9x2
x2
16
9x3 18x2 16x + 32
9x3 + 18x2
9
16x + 32
16x 32
2
9
0+ 32+
B
c2
0
32
B
c2
16
c
0
Write the quotient in standard form. (1.5 points) (Hint: The standard form of a complex number is
a + bi, where a and b are real numbers.)
6 7i
1 2i
6 7i
6 7i
=
1 2i
1 2i
3
16
18+
B
c2
0
2
18
1 + 2i
1 + 2i
=
6 + 5i 14i2
20 + 5i
=
= 4 + i.
2
1 4i
5
Find the domain of the function and identify any vertical or horizontal asymptotes. (2 points)
f (x) =
f =
x2 (x) 25
x2 4x 5
x2 25
(x + 5)(x 5)
=
.
2 4x 5
x
(x 5)(x + 1)
So, the domain is all real numbers except 5 and 1, since those are the two numbers which make the
denominator equal zero. The horizontal asymptote is at y = 1 because the highest power of x in both
the numerator and the demoninator is x2 , and each has coecient 1, so the horizontal asymptote is
1/1 = 1. The vertical asymptote is at x = 1. Note that there is not a vertical asymptote at x = 5
because the x 5 terms cancel, so there is just a hole in the function at x = 5.
University of Florida Honor Code:
On my honor, I have neither given nor received unauthorized aid in doing this assignment.
Signature