Questions and Answers
What should you do when asked to graph a polynomial of a degree higher than 3?
Use your calculator and check the positive and negative values.
What steps should you take when asked to find all the factors and solutions to a polynomial?
Use your calculator to find all whole-number x-intercepts, foil them together if needed, divide them by the original equation, and then factor the dividend.
How do you find Vertical Asymptotes?
Set the denominator equal to zero.
What is the method to find Horizontal Asymptotes?
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How do you find Holes in a rational function?
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What should you look for when asked to find a Slant Asymptote?
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What is the process to solve a Rational Function?
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How do you find the End Behavior of a polynomial function?
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What steps should you take when asked to solve an Inequality?
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Study Notes
Graphing Polynomials
- For polynomials of degree higher than 3, verify positive and negative values using a calculator.
- Identify x-intercepts and analyze end behavior.
Finding Factors and Solutions
- Utilize a calculator to determine all whole-number x-intercepts.
- Combine factors using the FOIL method if necessary, and divide them by the original polynomial.
- Ensure all radicals are simplified.
Vertical Asymptotes
- To locate vertical asymptotes, set the denominator of the function equal to zero.
Horizontal Asymptotes
- Determine horizontal asymptotes based on the degrees of the numerator and denominator:
- If degrees are equal, divide the leading coefficients.
- If the numerator's degree is smaller, the asymptote is y = 1.
- If the numerator's degree is larger, there is no horizontal asymptote.
Holes in Functions
- Identify holes by finding common factors in the numerator and denominator that can be canceled out.
Slant Asymptotes
- Check for an unfactored polynomial in the numerator or if the numerator is a squared term for slant asymptotes.
- The y-intercept for slant asymptotes is derived from the denominator.
Solving Rational Functions
- Multiply each term by the missing denominator terms and match all denominators.
- Eliminate denominators and solve the resulting equation.
End Behavior Analysis
- Use the leading coefficient to determine end behavior.
- For factored functions, multiply the largest degree terms within each factor, adding their degrees.
- Assess the sign based on the leading coefficient and whether the degree is even or odd.
Solving Inequalities
- Non-fractional inequalities are classified as "Polynomial":
- Simplify, find end behavior and x-intercepts, then graph or use an x/y chart for sign analysis.
- Fractional inequalities are "Rational":
- Simplify, find x-intercepts and x-asymptotes, then create an x/y chart.
- Analyze sign patterns to determine solution regions.
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Description
Test your understanding of polynomials and their graphs with this chapter review on Honors PreCalculus. These flashcards cover essential concepts such as graphing polynomials of various degrees and finding factors and solutions. Great for reinforcing your knowledge before exams!
