Module 4 DBA Algebra 2 Flashcards

Questions and Answers

Do you remember how to simplify a rational expression? What are the steps?

Step 1: Factor both the numerator and the denominator of the fraction. Step 2: Reduce the fraction. Step 3: Rewrite any remaining expressions.

How do you find the restrictions of a function?

Find the values of the variable that make the denominator equal to 0.

What is an asymptote?

Asymptotes are lines that a graph gets closer and closer to as x approaches a specific value or as x goes off to infinity.

What are the types of asymptotes?

Vertical, horizontal, oblique. Signup and view all the answers

How do you find the vertical asymptote?

Set the denominator equal to zero, simplify the fraction, and cancel out like terms on the top and the bottom. Signup and view all the answers

How do you find the horizontal asymptote?

Set the denominator equal to zero and solve for x. Signup and view all the answers

How do you find the oblique asymptote?

You must divide the numerator by the denominator using either long division or synthetic division. Signup and view all the answers

How do you find the discontinuity of a function?

Start by factoring the numerator and denominator of the function. A point of discontinuity occurs when a number is both a zero of the numerator and denominator. Signup and view all the answers

What is the difference between a discontinuity in a function and a vertical asymptote?

A discontinuity occurs when both the numerator and denominator equal zero; a vertical asymptote occurs when the denominator is zero but the numerator is not. Signup and view all the answers

How do you find zeroes?

Set the numerator of the function equal to zero and solve for the possible values. Signup and view all the answers

Do you remember how to solve a rational equation?

Step 1: Find the common denominator. Step 2: Multiply everything by the common denominator. Step 3: Simplify. Step 4: Check the answer(s) to make sure there isn't an extraneous solution. Signup and view all the answers

Study Notes

Simplifying Rational Expressions

Factor both the numerator and denominator of the fraction.
Reduce the fraction by canceling out common factors.
Rewrite any remaining expressions clearly.

Finding Restrictions of a Function

Identify variable values that cause the denominator to equal zero, as these values are not allowed.

Understanding Asymptotes

Asymptotes are lines that a graph approaches but never reaches, applicable as x approaches a specific value or infinity.

Types of Asymptotes

There are three main types: vertical, horizontal, and oblique asymptotes.

Finding Vertical Asymptotes

Set the denominator equal to zero and solve for x.
Simplify the fraction and cancel like terms if possible to identify vertical asymptotes.

Finding Horizontal Asymptotes

Determine horizontal asymptotes by examining the degrees of the numerator and denominator or by setting the denominator equal to zero.

Finding Oblique Asymptotes

Divide the numerator by the denominator using long division or synthetic division to derive the oblique asymptote.

Identifying Discontinuities

Factor the numerator and denominator to locate possible discontinuities.
A point of discontinuity occurs when a value is a zero for both the numerator and denominator. Validate by plugging the value into the simplified equation.

Distinction Between Discontinuity and Vertical Asymptote

Discontinuities occur where the function is not defined (zero in both numerator and denominator), while vertical asymptotes indicate where the function approaches infinity.

Finding Zeroes of a Function

Set the numerator equal to zero and solve for x to find the zeroes of the function.

Solving Rational Equations

Begin by finding a common denominator.
Multiply each term by the common denominator to eliminate fractions.
Simplify the resulting equation and check for extraneous solutions to ensure valid answers.

Description

Test your understanding of key concepts in Algebra 2 with these flashcards from Module 4. Each card focuses on essential topics such as rational expressions, function restrictions, and asymptotes. Perfect for reinforcing your algebra skills and preparing for exams!