Math 3 - Assess #J: 6.1 - 6.3 Graphing Rational Functions Flashcard

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What is a rational function?

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What are vertical asymptotes (V.A.)?

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Vertical asymptotes are lines x = a where the function approaches infinity or negative infinity as x approaches a. They occur where the denominator of a rational function is zero.

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What are horizontal asymptotes (H.A.)?

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Horizontal asymptotes are lines y = b that the graph of a function approaches as x approaches infinity or negative infinity. They indicate the end behavior of the function.

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How do you find the vertical asymptotes of a rational function?

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To find the vertical asymptotes, set the denominator of the rational function equal to zero and solve for x.

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How do you find the horizontal asymptotes of a rational function?

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To find horizontal asymptotes, compare the degrees of the numerator and denominator: If degree of P < degree of Q, H.A. is y = 0; if degree of P = degree of Q, H.A. is y = leading coefficient of P / leading coefficient of Q.

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The h-value is the horizontal shift of the graph. In this case, h = 5.

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What does the term 'branches' refer to in rational functions?

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Branches refer to the two separate parts of the graph of a rational function that extend towards infinity in opposite directions.

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The range is all real numbers except for the horizontal asymptote value, which is y = -5. Thus, the range is y ∈ ℝ, y ≠ -5.

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What is the significance of the h-value in graphing rational functions?

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The h-value indicates the horizontal shift of the graph, affecting where the function is centered along the x-axis.

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What is the relationship between the degree of the numerator and the degree of the denominator in determining asymptotes?

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The degree of the numerator compared to the degree of the denominator determines the presence and type of horizontal asymptotes.