Honors Algebra 2 - 8.3-8.6 review

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What is the process to solve rational equations?

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1. Find a common denominator. 2. Multiply both sides by the common denominator to eliminate fractions. 3. Solve the resulting equation. 4. Check for extraneous solutions.

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What is an extraneous solution?

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An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

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How do you identify vertical asymptotes in rational functions?

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Vertical asymptotes occur where the denominator of a rational function is zero and the numerator is not zero at those points.

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What is the horizontal asymptote of a rational function?

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The horizontal asymptote is determined by the degrees of the numerator and denominator: 1. If degree of numerator < degree of denominator, y = 0. 2. If degree of numerator = degree of denominator, y = leading coefficient of numerator / leading coefficient of denominator. 3. If degree of numerator > degree of denominator, there is no horizontal asymptote.

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The graph is a hyperbola that approaches the horizontal line y = -2 and has a vertical asymptote at x = 0.

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The graph is a hyperbola that approaches the horizontal line y = -2 and has a vertical asymptote at x = -2.

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What is the significance of the vertical asymptote in a graph?

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The vertical asymptote indicates the values of x where the function approaches infinity or negative infinity, and the function is undefined.

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