Algebra 2 - Illustrative Mathematics Chapters 1 & 2 Flashcards

Questions and Answers

What is an arithmetic sequence?

A sequence where no two terms are the same

A sequence where each term is found by multiplying the previous term by the same number

A sequence where each term is found by adding the same number to the previous term (correct)

A sequence of purely random numbers

What is the degree of a polynomial?

The greatest degree of any term in the polynomial.

What is end behavior in graphing?

The behavior of the graph as x approaches positive infinity or negative infinity.

What is a geometric sequence?

A sequence in which each term is found by multiplying the previous term by the same number Signup and view all the answers

What is a horizontal asymptote?

A horizontal line that the curve approaches but never reaches. Signup and view all the answers

What is an identity in algebra?

An equation that is true for all values of the variable. Signup and view all the answers

What is multiplicity concerning polynomials?

The power to which a factor occurs in the factored form of a polynomial. Signup and view all the answers

Define a polynomial function.

A function given by the sum of terms, each of which is a constant times a whole number power of the variable. Signup and view all the answers

What is a rational function?

A function defined by a fraction with polynomials in the numerator and the denominator. Signup and view all the answers

What is a relative maximum?

A point on the graph of a function where no other nearby points have a greater y-coordinate. Signup and view all the answers

What is a relative minimum?

A point on the graph of a function where no other nearby points have a lesser y-coordinate. Signup and view all the answers

What is a sequence?

A list of numbers, possibly going forever, like all the odd positive integers arranged in order. Signup and view all the answers

What is a term in a sequence?

One of the numbers in a sequence. Signup and view all the answers

Define a vertical asymptote.

A vertical line that a graph approaches but never crosses. Signup and view all the answers

What are integers?

Whole numbers that can be positive or negative, including zero Signup and view all the answers

What is an even number?

A number that is divisible by 2. Signup and view all the answers

What is an odd number?

A whole number ending with 1, 3, 5, 7, or 9 in the ones place. Signup and view all the answers

Define a rational number.

Any number that can be expressed as a ratio of two integers. Signup and view all the answers

What is a polynomial?

A mathematical expression that is the sum of a number of terms. Signup and view all the answers

What is a factor?

A number that is multiplied by another number to find a product. Signup and view all the answers

What does it mean to factor a polynomial?

To write the polynomial as a product of other polynomials. Signup and view all the answers

What is the graph of a function?

The collection of ordered pairs (x,f(x)) such that x is the domain of f. Signup and view all the answers

What are the intercepts of a graph?

The intercepts of a graph include the x and y-intercepts. Signup and view all the answers

What is the x-intercept?

The x-coordinate of a point where a graph crosses the x-axis. Signup and view all the answers

What is the y-intercept?

The y-coordinate of a point where a graph crosses the y-axis. Signup and view all the answers

What are the zeroes of a function?

Input values that produce an output of zero. Signup and view all the answers

Study Notes

Algebra 2 Key Concepts

Arithmetic Sequence: A sequence where each term is found by adding a constant value to the previous term.
Degree of a Polynomial: The highest exponent of any term within the polynomial indicates its degree.
End Behavior: Describes how the graph of a function behaves as the input approaches positive or negative infinity.
Geometric Sequence: A sequence in which each term is obtained by multiplying the prior term by a fixed constant.
Horizontal Asymptote: A line that represents where the graph approaches as it goes towards infinity but never actually intersects.
Identity: An equation that holds true for every possible value of the variable.
Multiplicity: Refers to the number of times a given factor appears in the polynomial's factored form.
Polynomial Function: A function expressed as the sum of multiple terms, each consisting of a constant multiplied by a variable raised to a non-negative integer power.
Rational Function: Defined as a function expressed as the ratio of two polynomials.
Relative Maximum: A point on a graph indicating that no nearby points have a higher y-coordinate.
Relative Minimum: A point on a graph where no nearby points have a lower y-coordinate.
Sequence: An ordered list of numbers that can continue indefinitely, such as the series of odd positive integers.
Term of a Sequence: An individual number within a sequence.
Vertical Asymptote: A vertical line that a graph approaches but never crosses, indicating behavior of the function.
Integer: Whole numbers that can be positive, negative, or zero.
Even Number: An integer that is divisible by 2 without remainder.
Odd Number: An integer whose last digit is 1, 3, 5, 7, or 9.
Rational Number: A number that can be expressed as a ratio between two integers.
Polynomial: An expression made by adding together several terms.
Factor: A number that divides another number exactly, contributing to the multiplication that yields a product.
Factoring a Polynomial: The process of expressing a polynomial as a product of simpler polynomials.
Graph of a Function: A visual representation of the relationship between the input values (domain) and their corresponding function outputs.
Intercepts of a Graph: Points where the graph intersects the axes; includes both x-intercepts and y-intercepts.
X-Intercept: The value of x at which the graph intersects the x-axis.
Y-Intercept: The value of y at which the graph intersects the y-axis.
Zeroes of a Function: Specific inputs that result in an output of zero for the function.

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Description

Test your knowledge of key concepts from Algebra 2 with these flashcards covering Illustrative Mathematics Chapters 1 and 2. Learn important definitions like arithmetic sequences and polynomial degrees to enhance your understanding of algebraic principles.