Algebra II Unit 2 Flashcards
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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?

<p>A polynomial of the first degree.</p> Signup and view all the answers

What is a linear inequality?

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

What is the standard form of a linear equation?

<p>An equation in the form Ax + By = C with not both A and B equal to zero.</p> 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.

<p>Degree</p> Signup and view all the answers

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

<p>expression</p> Signup and view all the answers

What is slope-intercept form?

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

What is a piecewise function?

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

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

<p>integer</p> Signup and view all the answers

What is absolute value?

<p>The distance of a number from zero.</p> Signup and view all the answers

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

<p>number</p> Signup and view all the answers

The absolute value function is a ______ linear function.

<p>piecewise</p> Signup and view all the answers

What is composition of functions?

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

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

<p>x</p> Signup and view all the answers

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

<p>nonzero</p> Signup and view all the answers

What is Gaussian elimination?

<p>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.</p> Signup and view all the answers

What is a linear system?

<p>A set of two or more linear equations or inequalities considered together.</p> 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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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.

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