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.

Tags

CCSS.HSA.REI.A.2

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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.

Tags

CCSS.HSA.REI.A.2

Front

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.

Tags

CCSS.HSA.REI.A.2

Front

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.

Tags

CCSS.HSA.REI.A.2

Front

What is the general form of a rational function?

Back

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CCSS.HSF-IF.C.7D

Front

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.

Front

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.

Tags

CCSS.HSF-IF.C.7D

Front

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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CCSS.HSF-IF.C.7D

Front

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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CCSS.HSA.APR.D.7

Front

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.

Tags

CCSS.HSF-IF.C.7D