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Precalculus: 4.1 Homework Notes
Precalculus: 4.1 Homework Notes
17
Mathematics
Undergraduate 1
10/28/2015

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Term
Define The Product Rule
Definition
When you are multiplying two terms that have the same base, you can just add their exponents to find your answer
Term
Define The Quotient Rule
Definition
You can subtract the power in the denominator from the power in the numerator.

[Power of Numerator - Power of Denominator]
Term
Define The Negative Exponent Rule
Definition
Negative exponents in the numerator get moved to the denominator and become positive exponents. Negative exponents in the denominator get moved to the numerator and become positive exponents. Only move the negative exponents.
Term
Define The Power Rule
Definition
To raise a power to a power you need to multiply the exponents.
Term
Define The Distributive Property of Exponents
Definition
If an exponent acts on single term in parentheses, we can distribute the exponent over the term.

If an exponent acts on multiple terms in parentheses (i.e. if there is a "+" or "-" sign in the parentheses), it cannot be distributed.
Term
How to Simplify An Expression So That No Negative Numbers End Up In the Result
(Assuming All Variables Are Non-Zero Numbers)
Definition
1.) Apply the Distributive Property of Exponents on The Numerator and Denominator
2.)Apply the Quotient Rule
3.)Apply the Negative Exponent Rule
4.)Simplify If Possible
Term
Define the Fractional Exponent Rule
Definition
When You Are Presented with (x^(m/n), you must place "x" to the "m" power of the "n" root or the "n" root of x to the the power of "m".
Term
How to Simplify An Exponential Expression With A Fractional Power
Definition
1.) Apply the Fractional Exponent Rule
2.) Simplify
Term
How To Identify An Exponential Function
Definition
They Have The Form y=(ab^x)
Where "a" and "b" are constants
and "x" is a variable.

"ab" is the base
"x" is the exponent
Term
How to Evaluate Exponential Functions
Definition
1.) Replace "x", with the given value for "x"
2.) Simplify The Expression By Applying the Rules of Exponents
Term
How To Graph An Exponential Function
Definition
1.) Choose Random Values For X
2.) Compute Values For Y Based On The Values For X
3.) Plot the Points
4.) Connect Them Into A Smooth Curve
Term
How to Match A Graph To An Exponential Function
Definition
1.) Graph the exponential functions given
2.) Find the exponential functions that match the given graph
Term
Horizontal Shifts That Go Right Are Formatted As...
Definition
x-m
Term
Horizontal Shifts That Go Left Are Formatted As...
Definition
x+m
Term
If in the graph of a function x approaches -infinity as y approaches 0 then the horizontal asymptote is...
Definition
y=0
Term
The Horizontal Asymptote is Where...
Definition
The Visual Representation of a Function on A graph stops Vertically on A Graph, Represented by the Y-value Where the Visual Representation of the Function Stops on The Graph.
Term
A Negative in Front of a Function Indicates A Reflection of The Graph Over The...
Definition
X-axis
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