College Algebra
MATH 140
Unit 2 Review
The test for Unit 2 covers material from sections 4.3, 4.4, 5.1, 5.2, 5.3, 5.5, 5.6, of your text, Algebra and
Trigonometry 8th Ed. by Sullivan. You are responsible for the topics covered in these sections. Be sure that you
review the homework and can do the problems assigned. Go over the quizzes, too.
In particular, be sure that you can do the following:
1. Recognize and graph the equation for a parabola.
Example
Graph
2.
. Identify intercepts and other important features.
Recognize and graph transformations of power functions based on your knowledge of the graph
for
Example
etc.
Graph
3.
. Identify intercepts and other important features.
Recognize and graph rational functions that are transformations of the basic
functions
Example
Graph
or
.
. Identify intercepts and other important features.
4. Graph a rational function by locating asymptotes and plotting a few points.
Example
Graph
5.
. Identify intercepts and other important features.
Given a polynomial
values of .
Example
, determine the power function that the graph for
Give the power function that approximates
represents for large
for large values of
.
6. Identify the number of complex zeros for a polynomial function.
Example
Indicate how many complex zeros there are for
.
Use Descartes’s Rule of Signs to determine the number of positive and negative real zeros of a
polynomial function.
Example
7.
Decide how many positive and negative real zeros there are for the function
.
8. Use the Rational Zeros Test to list all possible rational zeros for a polynomial function.
Example
List all possible rational zeros for
.
9. Given the zeros and/or factors for a polynomial function, write the formula for the function.
Example
Write the polynomial function for which
and
are factors, given that
and
.
10. When possible, find the zeros for a polynomial function using factoring and the quadratic formula.
Example
Find all zeros for
.
11. Use synthetic division (along with your knowledge of Descartes’s Rule of Signs and Rational Zeros Test)
to find all of the zeros for a third or fourth degree polynomial function (if it has one or more rational
roots).
Example
Find the zeros for
.