math 181 exam2
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m181_exam_2_fall_15.docMATHEMATICAL ANALYSIS I, MATH 181
Exam 2
Find the domain of each of the functions below.
(a)
12
7
1
)
(
2
+
-
=
x
x
x
g
(c)9
1
)
(
2
-
=
x
x
h
Graph each function below by finding the vertex and x and y intercepts.
(a)
16
)
(
2
+
=
x
x
f
(b)18
2
)
(
2
-
=
x
x
f
3. Graph the following functions.
(a)
(
)
3
+
-
=
x
x
f
(b)(
)
4
-
=
x
x
f
(c)(
)
2
5
-
+
=
x
x
f
4. Graph the following functions using a sign table.
(a)
(
)
3
2
2
-
+
=
x
x
x
f
(b)(
)
2
3
4
x
x
x
f
-
=
(c)(
)
4
4
-
=
x
x
f
5. Graph the following rational functions.
(a)
(
)
2
+
=
x
x
x
f
(b)(
)
1
4
+
-
=
x
x
x
f
6. Express each as a power of e.
(a)
3
5
e
e
-
(b)2
6
-
-
e
e
(c)3
2
3
4
e
e
e
e
-
-
4
)
(
+
=
x
x
f
7. Graph each function; label key points and/or identify characteristics such as asymptotes and behavior at infinity.(a) f(x) = 3 2x (b) f(x) = 3 -2x (c) f(x) = 23x+1 (d)
(
)
1
2
4
-
=
x
x
f
8. Solve the following exponential equations.
(a)
5
3
2
4
8
=
-
x
(b)2
1
2
27
9
-
+
=
x
x
(c)64
1
16
2
=
-
x
9. Find each logarithm without using a calculator.
(a)
5
1000
log
(b)10000
1
log
(c)3
10000
log
10. Find each logarithm without using a calculator.
(a)
3
ln
-
e
(b)5
1
ln
-
e
(c)4
ln
e
11. Use the properties of natural logarithms to simplify each function.
(a)
x
x
x
f
4
ln
4
3
ln
)
(
+
=
(b)(
)
(
)
4
5
2
ln
2
ln
)
(
x
x
x
g
-
=
(c)(
)
x
x
x
h
ln
3
ln
)
(
2
-
=
(d)
(
)
(
)
1
ln
3
ln
3
-
-
=
x
e
x
f
x
(e)(
)
(
)
x
x
e
e
x
g
ln
4
2
ln
-
=
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