Review Exam 2

REVIEW
EXAM
II

1.
Determine
whether
the
following
relations
on
 A = {1, 2, 3, 4} are
reflexive,


 symmetric and/or
transitive?

a. {
(2,
2),
(2,
3),
(2,
4),
(3,
2),
(3,
3),
(3,
4)
}

b. {
(1,
1),
(2,
2),
(3,
3)
}

c. {
(1,
3),
(1,
4),
(2,
3),
(2,
4),
(3,
1),
(3,
4)
}
 2.
Which
of
the
following
are
equivalent
relations
on
the
set
of
people?

If
not,
list
the
 property that
does
not
hold.

a. {
 (a,b) 
|
 a 
and
 b 
speak
a
common
language
}

b. 
{
 (a,b) 
|
 a 
and
 b 
have
the
same
sex
}
 3.
Determine
if
the
following
are
functions
from
 A = {1, 2, 3, 4} 
to
 B = {a,b, c, d} .
I
so
 determine if
the
function
is
one‐to‐one
and/or
onto.


1→ a
1→ a
1→ d
1→ d
1→ b
2→a
2→c
2→d







a.
 b.
 2 → c 
 


c.
 d.
 3→ b
3→ b
3→ d
3→ d
4→b
4→a
4→d
4→b

1→ a e.
 2 → b 

3→ c

4.
Find
the
domain
of
 g(x) =

x +1 x − 2 + x − 2 x +1

5.
Find
the
vertical
and
horizontal
asymptotes
of
 f (x) =

2x 2 − 4 x 2 − 5x + 6

6.
Find
the
inverse
of
 f (x) = 3x + 2 .
 7.
Calculate
 f  g 
and
 g  f 
where
 f (x) = 4x − 5 
and
 g(x) = x 2 .
 8.
Find



a.
 log 3 9 


b.
 log e

1 e5

c.
 log 4 64 


⎧x + 1
⎪
9.
Draw
the
graph
of
 f (x) = ⎨ 0
⎪ −x
⎩

x ≥1
−1< x