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?
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How do you find the vertical asymptote?
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How do you find the horizontal asymptote?
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How do you find the oblique asymptote?
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How do you find the discontinuity of a function?
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What is the difference between a discontinuity in a function and a vertical asymptote?
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How do you find zeroes?
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Do you remember how to solve a rational equation?
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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
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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!