College Algebra Quick Reference Sheet Page 2
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2College Algebra Quick Reference Sheet
Composition of Functions
Logarithm Definition
Arithmetic Sequence
Definition:
End Behavior of a Polynomial Function
th
Logarithm Example
n
term:
th
n
Behavior
a
n
partial sum:
Inverse Function
Let f be a one-to-one function with domain A and
odd
-1
range B. Then its inverse function f
has domain
Special Logarithms
B and range A. Each point with coordinates (a, b)
Common Logarithm
-1
.
in f has a corresponding point (b, a) in f
Geometric Sequence
odd
Natural Logarithm
Steps for Finding the Inverse Function
Definition:
where
th
1. Replace
with y.
n
term:
even
2. Interchange x and y.
th
n
partial sum:
3. Solve for y.
4. Replace y with
.
Logarithm Properties
even
Inverse Function Property
Let f be a one-to-one function with domain A and
-1
range B. The inverse function f
satisfies the
Finance Formulas
Multiplicities of Real Zeros of a
following cancelation properties.
For all formulas:
Polynomial Function
A
is the future amount
f
m
Behavior
A
is the present amount
p
t is the number of years
odd
Crosses the x-axis
r is the annual interest rate (decimal)
Laws of Logarithms
n is the number of periods in a year
even
Touches the x-axis
Radical Properties
Product Rule
i = r/n is the interest rate per period
R is the periodic payment amount
Quotient Rule
Simple Interest
Rational Functions
Power Rule
Vertical Asymptotes (No Holes)
If a factor (x-a) appears in the denominator (but
Logarithm Change of Base Formula
Compound Interest
not in the numerator), the line x=a is a vertical
asymptote.
Horizontal Asymptote
If the degree of the numerator is less than the
Continuously Compounded Interest
degree of the denominator, then there is a
Steps to Solve an Exponential Equation
horizontal asymptote at y = 0 (x-axis).
Exponent Laws and Properties
1. Isolate the exponential function.
If the degree of the numerator is the same as the
2. Take the appropriate logarithm of both sides.
degree of the denominator, then there is a
Future Value of an Annuity
horizontal asymptote at y= (leading coefficient of
3. Use the inverse function property.
numerator) / (leading coefficient of denominator).
4. Solve for the variable.
If the degree of the numerator is greater than the
degree of the denominator, then there is not a
Present Value of an Annuity
horizontal asymptote.
Steps to Solve a Logarithmic Equation
1. Isolate the logarithmic function.
2. Use the appropriate base to raise both sides.
Payment Amount of a Loan
3. Use the inverse function property.
4. Solve for the variable.
5. Remove false answers (look for domain errors).
Page 2
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