Rational functions
9 videos
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Pre-Calculus - What Are Rational Functions?
Learn what rational functions are, how they're formed by dividing polynomials, and discover their key features: zeros, vertical asymptotes, and horizontal asymptotes.
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Pre-Calculus - Simplifying Rational Expressions
Learn to simplify rational expressions in three steps: factor the numerator and denominator, cancel common factors, and state restrictions. Includes worked examples.
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Pre-Calculus - End Behavior and Horizontal Asymptotes
Learn how to find horizontal asymptotes of rational functions by comparing degrees of numerator and denominator, plus analyzing leading coefficients.
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Pre-Calculus - Vertical Asymptotes vs. Removable Discontinuities
Learn how factoring rational functions reveals whether dividing by zero creates a hole or vertical asymptote. Canceling factors make holes; non-canceling make asymptotes.
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Pre-Calculus - Finding Zeros, Asymptotes, and Holes — Practice
Learn to find holes, zeros, and vertical asymptotes in rational functions by factoring and simplifying. Step-by-step analysis of f(x) = (x²+x-6)/(x²-4).
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Pre-Calculus - Graphing Rational Functions Step by Step
Learn a step-by-step system to graph rational functions by factoring, identifying key features like asymptotes and holes, then sketching the curve.
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Pre-Calculus - Multiplying and Dividing Rational Expressions
Learn to multiply and divide rational expressions by factoring, canceling common terms, and tracking domain restrictions, just like working with regular fractions.
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Pre-Calculus - Adding and Subtracting Rational Expressions
Learn how to add rational expressions with different denominators by finding the LCD, rewriting fractions, and combining numerators—just like adding fractions.
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Pre-Calculus - Combined Rates Word Problems
Learn how to solve work rate problems by converting time to rates. Discover the formula: 1/a + 1/b = 1/t to find combined work time when two people work together.