MAP 103: Proficiency Algebra
Homework #5
DUE: THURSDAY, OCTOBER 8, 2009
1.
Let
X
=
{
0
,
1
,
2
,
3
,
4
}
and
Y
=
{
0
,
2
,
4
,
6
,
8
}
.
Suppose
f
:
X
→
Y
is relation between the two sets
so that the set
X
is the domain of the relation and
Y
is the range. Could
f
be a function?
2.
Find the equation of a linear function in the form
f
(
x
) =
ax
+
b
satisfying that
f
(1) = 3 and
f
(4) = 7
.
Using your function, find
f
(

1)
.
What is the domain of
f
?
3.
On the interval

5
6
x
6
5
,
graph the relation
y
=

x

.
(a) From definitions, is
y
=

x

a function?
(b) Is
y
=

x

onetoone?
(c) Is
y
=

x

onto?
4.
Let Γ
f
denote the graph of a function
f.
Determine if following sets give functions.
(a) Γ
f
=
{
(
x, y
)
∈
R
×
R

y
=
x
+ 1
}
(b) Γ
f
=
{
(
x, y
)
∈
R
×
R

y
=
x
2
+
x
}
(c) Γ
f
=
{
(
x, y
)
∈
R
×
R

y
=

x

x
}
(d) Γ
f
=
{
(
x, y
)
∈
R
×
R

y
2
=
x
2
}
5.
For each of the functions below, find its respective domain.
(a)
f
(
x
) =
x
2
+ 2
x
+ 1
(b)
f
(
x
) = 1 +
√
1

x
(c)
f
(
x
) =
√
x
2

1
(d)
f
(
x
) =
5
x
4
x
+1
6.
Let
f
(
x
) =
(
x
+ 1
x >
2

x
+ 1
x
6
2
.
Find
f
(0) and
f
(2)
.
7.
Sketch the graph of a function
y
=
f
(
x
) that satisfies the following properties:
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 Staff
 ΓF, Proﬁciency Algebra Homework

Click to edit the document details