Algebra 2 Module 5 DBA Flashcards

Questions and Answers

What is a rational expression?

A fraction with a polynomial in the numerator and denominator (correct)

A fraction that cannot be simplified

A whole number

An irrational number

What does the difference of squares refer to?

two perfect square terms being subtracted

What is a perfect square trinomial?

an expression consisting of three terms where the first and last terms are perfect squares, and the middle term is twice the product of the square roots of those terms

The steps to simplifying rational expressions include factoring the numerator and denominator, identifying the restrictions, and ___

simplifying Signup and view all the answers

What is a discontinuity?

a point on the graph of a rational function where it doesn't exist Signup and view all the answers

What is an asymptote?

an imaginary line running alongside the graph of a rational function Signup and view all the answers

What are vertical asymptotes?

imaginary lines that continue forever up and down the coordinate plane Signup and view all the answers

What are oblique asymptotes?

lines that are slanted or lie along a diagonal Signup and view all the answers

What is an extraneous solution?

a solution to a radical equation that does not satisfy the original equation Signup and view all the answers

What is a non-extraneous solution?

a solution that does satisfy the original equation Signup and view all the answers

Study Notes

Rational Expressions

Defined as a fraction containing a polynomial in both the numerator and the denominator.

Difference of Squares

Formed by subtracting two perfect square terms.

Perfect Square Trinomial

Consists of three terms.
The first and last terms are perfect squares.
The middle term equals twice the product of the square roots of the first and last terms.

Steps to Simplifying Rational Expressions

Factor both the numerator and denominator when possible.
Identify any restrictions on the variables.
Simplify the expression by canceling common factors.

Discontinuity

Refers to points in a rational function's graph where it does not exist.

Asymptote

An imaginary line that approaches the graph of a rational function but never touches it.

Vertical Asymptotes

These imaginary lines extend infinitely upwards and downwards along the coordinate plane.

Oblique Asymptotes

Lines that are neither vertical nor horizontal.
They extend diagonally along the graph of a function.

Extraneous Solution

A solution derived from a radical equation that does not satisfy the original equation.

Non-extraneous Solution

A solution that satisfies the original equation, confirming its validity.

Description

Test your knowledge with these flashcards from Algebra 2 Module 5. This quiz covers key concepts such as rational expressions, difference of squares, and perfect square trinomials. Perfect for reviewing essential algebraic expressions and their definitions.