Podcast
Questions and Answers
Do you remember how to simplify a rational expression? What are the steps?
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?
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?
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?
What are the types of asymptotes?
Signup and view all the answers
How do you find the vertical asymptote?
How do you find the vertical asymptote?
Signup and view all the answers
How do you find the horizontal asymptote?
How do you find the horizontal asymptote?
Signup and view all the answers
How do you find the oblique asymptote?
How do you find the oblique asymptote?
Signup and view all the answers
How do you find the discontinuity of a function?
How do you find the discontinuity of a function?
Signup and view all the answers
What is the difference between a discontinuity in a function and a vertical asymptote?
What is the difference between a discontinuity in a function and a vertical asymptote?
Signup and view all the answers
How do you find zeroes?
How do you find zeroes?
Signup and view all the answers
Do you remember how to solve a rational equation?
Do you remember how to solve a rational equation?
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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!
