Evaluating Polynomial and Rational Functions
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ge_ca_lesson_6.1_assignment_handout.doc
College Algebra
Assignment Handout
Assignment 6.1: Evaluating Polynomial and Rational Functions
Complete the following problems: Be sure to show all work.
1) Find the vertex and intercepts of the following quadratic functions. State whether the parabola opens up or down. Use this information to sketch the graph.
a.
4
)
7
(
3
)
(
2
+
-
=
x
x
f
b.
5
6
)
(
2
-
+
-
=
x
x
x
f
c.
1
2
1
)
(
2
-
-
=
x
x
x
f
2) You have 300 feet of fencing to enclose a rectangular lot. Find the dimensions of the rectangle that will maximize the enclosed area. What is the largest area that can be enclosed?
3) Use the leading coefficient test to determine the end behavior of the following polynomial functions.
a.
1
7
)
(
2
3
-
+
+
=
x
x
x
x
f
b.
7
3
4
4
)
(
2
3
4
-
+
+
+
-
=
x
x
x
x
x
f
c.
543
()436
fxxxxx
=-++--
4) Use the intermediate value theorem to show each polynomial has a real zero between the given integers.
a.
105
9
)
(
2
3
-
-
+
=
x
x
x
x
f
; between 1 and 4b.
20
68
23
3
)
(
2
3
-
-
-
=
x
x
x
x
f
; between –1 and 05) Divide using either long division or synthetic division.
a.
)
1
(
)
12
4
7
(
2
3
+
¸
+
+
-
x
x
x
x
b.
)
1
2
(
)
4
7
6
2
(
2
3
4
5
+
¸
-
-
+
+
+
x
x
x
x
x
x
6) Find all zeros of polynomial functions given. Use whatever method(s) that you choose.
a.
12
11
2
)
(
2
3
-
-
+
=
x
x
x
x
f
b.
20
41
2
)
(
2
3
-
-
-
=
x
x
x
x
f
c.
6
5
)
(
2
3
4
-
+
-
+
=
x
x
x
x
x
f
College Algebra Handout Assignment 6.1, V2.4 Page 1 of 1 2/20/2012
© 2012 Pearson Education
