Algebra II Unit 2 Flashcards

Questions and Answers

What is the degree of a polynomial?

The degree of the term with the highest degree in a polynomial.

What is the degree of a term of a polynomial?

The sum of the exponents on the variables in a term of a polynomial.

What is a linear equation?

A mathematical statement that two linear expressions, or a linear expression and a constant, are equal.

What is a linear expression?

A polynomial of the first degree. Signup and view all the answers

What is a linear inequality?

A mathematical statement that two linear expressions, or a linear expression and a constant, are not equal. Signup and view all the answers

What is the standard form of a linear equation?

An equation in the form Ax + By = C with not both A and B equal to zero. Signup and view all the answers

The ______ is the highest power or the sum of the powers (exponents) on the variables of a term in a polynomial.

Degree Signup and view all the answers

A linear ______ is a polynomial equation of the first degree.

expression Signup and view all the answers

What is slope-intercept form?

A linear equation of the form y = mx + b where m is the slope and b is the y-intercept. Signup and view all the answers

What is a piecewise function?

A function defined differently on different intervals of the function's domain. Signup and view all the answers

An example of a piecewise function is the greatest ______ function.

integer Signup and view all the answers

What is absolute value?

The distance of a number from zero. Signup and view all the answers

The absolute value of a positive number is the ______ itself.

number Signup and view all the answers

The absolute value function is a ______ linear function.

piecewise Signup and view all the answers

What is composition of functions?

The process of combining two functions using the output of one function as the input of another function. Signup and view all the answers

A function composed with its inverse function will always equal ______.

x Signup and view all the answers

Every linear function with a ______ slope will have an inverse function.

nonzero Signup and view all the answers

What is Gaussian elimination?

A method of solving a system of equations or inequalities by systematically adding or subtracting a multiple of one equation or inequality to a multiple of another equation to eliminate a variable. Signup and view all the answers

What is a linear system?

A set of two or more linear equations or inequalities considered together. Signup and view all the answers

Study Notes

Polynomial Definitions

The degree of a polynomial is determined by the term with the highest degree.
The degree of a term of a polynomial is calculated by summing the exponents of the variables in that term.

Linear Equations and Expressions

A linear equation expresses equality between two linear expressions or between a linear expression and a constant.
A linear expression is defined as a polynomial of the first degree.

Inequalities

A linear inequality indicates that two linear expressions or a linear expression and a constant are not equal.

Standard Form

The standard form of a linear equation is expressed as Ax + By = C, where A and B cannot both be zero.

Slope-Intercept Form

The slope-intercept form of a linear equation is characterized by y = mx + b, where m represents the slope and b represents the y-intercept.

Functions and Their Definitions

A piecewise function operates differently over various intervals within its domain.
An example of a piecewise function is the greatest integer function, which rounds down to the nearest integer.

Absolute Value

The absolute value measures the distance of a number from zero on the number line.
For any positive number, the absolute value equates to the number itself.
The absolute value function is classified as a piecewise linear function due to its differing treatments based on input values.

Composition of Functions

The composition of functions merges two functions by using the output from one as the input for another.
When a function is composed with its inverse, the result will always yield x, indicating a return to the original input.
Only linear functions with a nonzero slope possess an inverse function.

Solving Systems of Equations

Gaussian elimination is a strategic procedure for solving systems of equations by systematically eliminating variables through additive or subtractive operations on the equations.

Linear Systems

A linear system is a collection of two or more linear equations or inequalities viewed collectively.

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Description

Test your knowledge of linear equations, inequalities, and polynomial functions with this set of flashcards. Each card features key terms and their definitions, making it a great tool for mastering the concepts in Algebra II Unit 2.