Algebra I Ch. 6 Vocabulary

Question 1

Using Zero & Negative Exponents Core Concept

Answer 1

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

Question 2

Power

Answer 2

an infinite series of the form where aₙ represents the coefficient of the nth term and c is a constant.

Question 3

Exponent

Answer 3

A mathematical notation indicating the number of times a quantity is multiplied by itself.

Question 4

Scientific Notations

Answer 4

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.

Question 5

Base

Answer 5

The total count of digits used to express numbers in a number system.

Question 6

Product of Power Property

Answer 6

To multiply powers having the same base, add the exponents.

Question 7

Quotient of Power Property

Answer 7

When dividing two powers with the same base, we subtract the exponents.

Question 8

Power of Power Property

Answer 8

To find a power of a power, multiply the exponents/(a^m)^n = a^mn

Question 9

Nth Root of a

Answer 9

For an integer n greater than 1, if b^n = a, then b is an nth root of a.

Question 10

Radical

Answer 10

The √ symbol that is used to denote square root or nth roots/an expression containing a square root.

Question 11

Index of Radical

Answer 11

A numeral or letter written above and to the left of the radical sign to indicate the required root.

Question 12

Square foot

Answer 12

a unit of area equal to one foot by one foot square

Question 13

Index

Answer 13

The power or exponent which is raised to a number or a variable.

Question 14

Real nth Roots of “a” Core Concept

Answer 14

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.

Question 15

Rational Exponents

Answer 15

Expressions will have the fractional numbers as power. The general form is x a/b.

Question 16

Exponential Functions

Answer 16

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.

Question 17

Graphing Exponential Functions Core Concept

Answer 17

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.

Question 18

Exponential Growth

Answer 18

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.

Question 19

Exponential Growth Function

Answer 19

A function of the form y=ab^x, where b is greater than 1 and a is greater than zero

Question 20

Exponential Decay

Answer 20

a decrease that follows an exponential function/y=a(1-r)^t

Question 21

Exponential Decay Function

Answer 21

y = ab^x if a > 0 and 0 < b < 1

Question 22

Compound Interest

Answer 22

an equation in which the variables occur as exponents/y=ab^x

Question 23

Exponential Equation

Answer 23

an equation in which the variables occur as exponents/y=ab^x

Question 24

Property of Equality for Exponential Equations

Answer 24

When the bases on both sides of an exponential equation are equal, then the exponents must also be equal.

Question 25

Solving Exponential Equations w/ Unlike Bases

Answer 25

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.

Question 26

Geometric Sequences

Answer 26

There is a pattern in which you multiply or divide by a common number.

Question 27

Common Ratio

Answer 27

Another name for the multiplier or generator of a geometric sequence

Question 28

Equation for a Geometric Sequence

Answer 28

an=a1(r)^n-1

Question 29

Recursive Rule

Answer 29

A rule for a sequence in which one or more previous terms are used to generate the next term.

Question 30

Explicit Rule

Answer 30

A rule that defines the

nth term an, or a general term, of a

sequence as a function of n.

Question 31

Recursive Equation for an Arithmetic Sequence

Answer 31

an=an-1+d

Question 32

Recursive Equation for a Geometric Sequence

Answer 32

an=r(an-1)