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Concept Review: Math 107 Final Exam
1. Solving equations:
Factor: (by grouping or by rational zeros theorem for polynomials)
Understand and utilize algebraic operations (e.g. combining fractions, laws of exponents, laws of
logarithms, reducing exponentials, getting rid of logs, properties of inverse functions, completing the
square, .
..)
Plug variables into a function (average rate of change, exponential models,.
..)
Check solutions against the domain restrictions
2. Solving inequalities:
Use when determining domain restrictions
Know when the direction changes (e.g. absolute value inequalities: think bounded or unbounded)
3. Domains:
Use interval notation except for with inﬁnite breaks (e.g. tan(
x
)
,
cot(
x
)
, ...
)
Start from original equation (not simpliﬁed version)
List how you restrict the domains of these three types of problems:
*Even roots (e.g.
p
f
(
x
)
=
⇒
f
(
x
)
≥
0)
*Dividing by zero: (e.g.
1

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