Questions and Answers
What is the first step in finding asymptotes?
How do you find X-intercepts?
Set numerator equal to zero and solve
How do you find the Y-intercept?
Let X equal zero
How do you find vertical asymptotes?
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How do you find the horizontal asymptote?
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How do you find the slant asymptote?
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Study Notes
Steps to Analyze Rational Functions
- Simplify the function by canceling any common factors.
- Identify X-intercepts by setting the numerator equal to zero and solving for X.
- Determine the Y-intercept by substituting X with zero in the function.
- Locate vertical asymptotes by setting the denominator equal to zero and solving for X.
- Assess horizontal asymptotes based on the degrees of the numerator and denominator:
- No horizontal asymptote if the numerator's degree is higher.
- Horizontal asymptote at y=0 if the denominator's degree is higher.
- If degrees are the same, the horizontal asymptote is the ratio of the leading coefficients.
- Discover slant asymptotes which occur only when the numerator's degree is one greater than the denominator's; use synthetic division to find their equation.
- Check for holes in the graph that occur at canceled factors in the rational function.
X-Intercepts
- Found by setting the numerator equal to zero and solving for the respective values of X.
Y-Intercepts
- Determined by evaluating the function when X is set to zero.
Vertical Asymptotes
- Established by solving the equation obtained from setting the denominator equal to zero.
Horizontal Asymptotes
- Baseline rules for identifying horizontal asymptotes depend on the relative degrees of the polynomials involved.
Slant Asymptotes
- Unique to situations where the numerator’s degree is precisely one higher than the denominator’s, applicable only when performing synthetic division.
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Description
This quiz covers the steps to analyze rational functions in algebra. You will learn how to simplify rational expressions, find X and Y intercepts, identify asymptotes, and check for holes in the graph. Perfect for students looking to master rational function analysis.
