Algebra 2 Chapter 8 Flashcards

Questions and Answers

What is combined variation?

When one quantity varies directly with respect to two or more quantities. (correct)

A type of rational expression.

When two quantities are inversely related.

When one quantity varies directly with respect to a single quantity.

What is a complex fraction?

A rational expression whose numerator and/or denominator contains a fraction.

What is the constant of variation (K)?

K = constant of variation.

Define direct variation.

A relationship in which one variable quantity increases as another variable quantity also increases. Signup and view all the answers

What is a horizontal asymptote?

A line that can be crossed, and the graphs follow it on the far left and far right. Signup and view all the answers

What is a hyperbola?

f(x) = 1/x. Signup and view all the answers

What is inverse variation?

A relationship in which one variable quantity increases as another variable quantity decreases. Signup and view all the answers

Define joint variation.

A relationship that occurs when a quantity varies directly with the product of two or more other quantities. Signup and view all the answers

What is an oblique asymptote?

An asymptote that is neither horizontal nor vertical. Signup and view all the answers

What is a point of discontinuity?

A point where the function is not continuous. Signup and view all the answers

What is a rational equation?

An equation containing one or more rational expressions. Signup and view all the answers

Define a rational expression.

The quotient of two polynomials. Signup and view all the answers

What is a rational function?

A function which is the ratio of two polynomials. Signup and view all the answers

What is a rational inequality?

Inequalities that contain one or more rational expressions. Signup and view all the answers

What is the reciprocal function?

The parent function for the function family of inverse variation equations. Signup and view all the answers

Define a vertical asymptote.

A line that can't be crossed, where the graphs follow the line. Signup and view all the answers

What is a weighted average?

The mean of a set of numbers in which some numbers carry more weight than others. Signup and view all the answers

Study Notes

Combined Variation

Describes scenarios where one variable changes directly in relation to two or more other variables.

Complex Fraction

Defined as a rational expression that includes a fraction within its numerator and/or denominator.

Constant of Variation

Represented as K, it indicates the rate at which one quantity varies in relation to another.

Direct Variation

A mathematical relationship where an increase in one variable leads to an increase in another, represented by the equation Y = kX.

Horizontal Asymptote

A line that may be intersected by a graph, which approaches the line on the left and right sides but does not necessarily stay close.

Hyperbola

Defined by the equation f(x) = 1/x, serving as the reciprocal function in algebra.

Inverse Variation

Illustrates a relationship where one variable increases while the other decreases, maintaining a constant product, expressed by the equation y = k/x.

Joint Variation

A form of variation where a variable changes directly in proportion to the product of two or more other variables.

Oblique Asymptote

Also known as a slant asymptote, it represents an asymptote that is neither horizontal nor vertical.

Point of Discontinuity

Identified as a specific point where a function lacks continuity.

Rational Equation

An equation featuring one or more rational expressions, often complex in nature.

Rational Expression

Defined as the quotient of two polynomials, forming a fundamental aspect of rational functions.

Rational Function

A function characterized by being the ratio of two polynomial expressions.

Rational Inequality

A type of inequality that consists of one or more rational expressions, often requiring specific solutions.

Reciprocal Function

The parent function of inverse variation equations, forming the basis for understanding this type of relationship.

Vertical Asymptote

A line that a graph cannot cross, with the graph approaching the line without intersecting it.

Weighted Average

The mean of a group of numbers, where some numbers are given more significance compared to others, affecting the overall average calculation.

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Description

Test your knowledge on key concepts from Algebra 2 Chapter 8 with these flashcards. Each card features a term and its definition, helping you to reinforce your understanding of combined variation, complex fractions, and more. Perfect for exam preparation or quick revision.