Barry University
MAT 109  Precalculus Mathematics I
MAT 109 Final Exam Study Guide
n
th
Semester
Writer: ”Lew” Sterling Jr.
Objective:
The objective of this final exam study guide is to prepare yourself for
the upcoming final exam for Precalculus Mathematics I. Take your time when you
read each question and what you need to do in order to solve various problems that
you have learned during the duration of taking Precalculus Mathematics I.
General Instructions:
Read each question carefully. Show all work to show that
you understood how to solve each problems correctly. Just remember to take your
time and for some problems, there are more than one way to solve some problems
(and especially when it comes to establishing the identities).
In this final exam study guide for Precalculus Mathematics I, you will have to un
derstand how to do the following things to get ready for the actual final exam of this
respective mathematics course:
•
Finding the domain of functions
•
Finding the intercepts of functions
•
Finding the (horizontal and vertical) asymptotes of functions
•
Finding the average rate of change
•
Finding inverse functions
•
Finding the difference quotient of functions
•
Expanding logarithmic expressions
•
Solving logarithmic and exponential equations
•
Graphing functions
•
Solving polynomic and rational inequalities
•
Convert logarithms into exponential form
•
Constructing polynomials
•
Evaluating functions
•
Solving functions
•
Finding the zeros of polynomic and rational functions
•
Function composition
•
Computing functions using function composition
•
Finding values of logarithms
•
Finding the equation of an ellipse
•
Exponential growth
•
Dividing and factorizing polynomic expressions
•
Finding the equation of a parabola
Section A.
Find the domain of each function.
When it comes to finding the domain of various functions, you have to know what type
of function you are dealing with in order to how to set and find its domain, which means
doing the following:
Function
Domain
Constant
Domain =
<
Polynomial
Domain =
<
Rational
Set denominator
6
= 0
Radical
Set inside
≥
0
Logarithmic
Set inside
>
0
1.
f
(
x
) =
2
x
+3
x
2

5
x
+6
When it comes to finding the domain of a rational function, you have to set the de
nominator unequal to 0 (since you are finding the undefined, or unknown, points of the
function), which means that you are going to set
x
2

5
x
+ 6 to 0, which means doing
the following:
x
2

5
x
+ 6
6
= 0
x
2

2
x

3
x
+ 6
6
= 0
(
x
2

2
x
) + (

3
x
+ 6)
6
= 0
x
(
x

2)

3 (
x

2)
6
= 0
(
x

2) (
x

3)
6
= 0
x

2 = 0
x

3
6
= 0
x

2 + 2
6
= 0 + 2
x

3 + 3
6
= 0 + 3
x
6
= 2
x
6
= 3
{
x

x
6
=
2
,
3
}
2.
f
(
x
) =
√
2
x

6
When it comes to finding the domain of a square root function, you have to set the
interior of the radical greater than or equal to 0, which means doing the following:
2
x

6
≥
0
2
x

6 + 6
≥
0 + 6
2
x
≥
6
2
x
2
≥
6
2
x
≥
3
{
x

x
≥
3
}
3.
f
(
x
) =
1
√
2
x

6
When it comes to finding the domain of a rational function, you have to set the de
nominator greater than 0, which means that you are going to set
√
2
x

6 to 0, which
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