Algebra I Ch. 6 Vocabulary Flashcards
Using Zero & Negative Exponents Core Concept
Zero Exponent
Words: For any nonzero a, a to 0 power = 1. The power 0 tiny 0 is undefined.
Numbers: 4 tiny 0 = 1 Algebra: a tiny 0 = 1, where a slashed equal sign 0
Negative Exponents
Words: For any integer n and any nonzero number a, a tiny negative n is the reciprocal of a tiny n.
Numbers: 4 tiny negative 2 = 1/4 tiny 2 Algebra: a tiny negative n = 1/a tiny n, where a slashed equal sign 0
Power
an infinite series of the form where aₙ represents the coefficient of the nth term and c is a constant.
Exponent
A mathematical notation indicating the number of times a quantity is multiplied by itself.
Scientific Notations
A number in the form of a x 10^n, where n is an integer and 1 is less than or equal to a which is less than 10.
Base
The total count of digits used to express numbers in a number system.
Product of Power Property
To multiply powers having the same base, add the exponents.
Quotient of Power Property
When dividing two powers with the same base, we subtract the exponents.
Power of Power Property
To find a power of a power, multiply the exponents/(a^m)^n = a^mn
Nth Root of a
For an integer n greater than 1, if b^n = a, then b is an nth root of a.
Radical
The √ symbol that is used to denote square root or nth roots/an expression containing a square root.
Index of Radical
A numeral or letter written above and to the left of the radical sign to indicate the required root.
Square foot
a unit of area equal to one foot by one foot square
Index
The power or exponent which is raised to a number or a variable.
Real nth Roots of “a” Core Concept
If a is a real number with at least one nth root, then the principal nth root of a is the number with the same sign as a that, when raised to the nth power, equals a . The principal nth root of a is written as n√a , where n is a positive integer greater than or equal to 2.
Rational Exponents
Expressions will have the fractional numbers as power. The general form is x a/b.
Exponential Functions
a function of the form y = a*b^x, where both a and b are greater than 0 and b is not equal to 1.
Graphing Exponential Functions Core Concept
The graph of the function f(x)=bx f ( x ) = b x has a y-intercept at (0,1) , domain of (−∞,∞) , range of (0,∞) , and horizontal asymptote of y=0 . If b>1 , the function is increasing. The left tail of the graph will approach the asymptote y=0 , and the right tail will increase without bound.
Exponential Growth
Process that increases quantity over time. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself.
Exponential Growth Function
A function of the form y=ab^x, where b is greater than 1 and a is greater than zero
Exponential Decay
a decrease that follows an exponential function/y=a(1-r)^t
Exponential Decay Function
y = ab^x if a > 0 and 0 < b < 1
Compound Interest
an equation in which the variables occur as exponents/y=ab^x
Exponential Equation
an equation in which the variables occur as exponents/y=ab^x
Property of Equality for Exponential Equations
When the bases on both sides of an exponential equation are equal, then the exponents must also be equal.
Solving Exponential Equations w/ Unlike Bases
Apply the logarithm to both sides of the equation. If one of the terms in the equation has base 10 , use the common logarithm. Use the rules of logarithms to solve for the unknown.
Geometric Sequences
There is a pattern in which you multiply or divide by a common number.
Common Ratio
Another name for the multiplier or generator of a geometric sequence
Equation for a Geometric Sequence
an=a1(r)^n-1
Recursive Rule
A rule for a sequence in which one or more previous terms are used to generate the next term.
Explicit Rule
A rule that defines the
nth term an, or a general term, of a
sequence as a function of n.
Recursive Equation for an Arithmetic Sequence
an=an-1+d
Recursive Equation for a Geometric Sequence
an=r(an-1)
