Unit 8 Rationals Test Review

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What is a rational function?

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A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

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What is the process to solve a rational equation?

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To solve a rational equation, find a common denominator, eliminate the denominators by multiplying both sides by it, and then solve the resulting polynomial equation.

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What is an asymptote in the context of rational functions?

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An asymptote is a line that a graph approaches but never touches. There are vertical, horizontal, and slant asymptotes.

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How do you find vertical asymptotes of a rational function?

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Vertical asymptotes occur where the denominator of the rational function is equal to zero, provided the numerator is not also zero at those points.

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What is a slant (oblique) asymptote?

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A slant asymptote occurs when the degree of the numerator is exactly one more than the degree of the denominator. It can be found using polynomial long division.

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How do you subtract rational expressions?

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To subtract rational expressions, find a common denominator, rewrite each fraction with that denominator, and then subtract the numerators.

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What is the formula for finding the average speed of a canoe in still water given upstream and downstream speeds?

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What is the significance of the current in a river when calculating canoe speed?

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The current affects the effective speed of the canoe when going upstream (slower) and downstream (faster), which must be accounted for in calculations.

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What does it mean if a rational equation has no solution?

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