Warm Up: Rational Equations

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What is a rational equation?

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A rational equation is an equation that involves at least one rational expression, which is a fraction where the numerator and/or denominator are polynomials.

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What does it mean if a rational equation has 'No Solution'?

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'No Solution' means that there are no values for the variable that will satisfy the equation, often due to a contradiction or division by zero.

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How do you solve a rational equation?

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To solve a rational equation, find a common denominator, eliminate the fractions by multiplying through by that denominator, and then solve the resulting polynomial equation.

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What is the importance of checking for extraneous solutions in rational equations?

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Checking for extraneous solutions is important because the process of solving can introduce solutions that do not satisfy the original equation.

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What is the general form of a rational function?

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What is the domain of a rational function?

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The domain of a rational function includes all real numbers except where the denominator equals zero.

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How do you find vertical asymptotes of a rational function?

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Vertical asymptotes occur at the values of x that make the denominator zero, provided that these values do not also make the numerator zero.

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What is a horizontal asymptote?

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A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches infinity or negative infinity.

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What is the process for adding or subtracting rational expressions?

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To add or subtract rational expressions, find a common denominator, rewrite each expression with that denominator, and then combine the numerators.

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What is the significance of the degree of the numerator and denominator in rational functions?

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The degree of the numerator and denominator determines the behavior of the function, including the presence of horizontal asymptotes.