Rational Function Transformations

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What is a vertical asymptote?

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A vertical asymptote is a line x = a where a rational function approaches infinity or negative infinity as the input approaches a. It indicates values that the function cannot take.

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It shifts left 3 units.

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The asymptotes are x = 0 (vertical) and y = 0 (horizontal).

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What is a horizontal asymptote?

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

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Adding a constant shifts the graph vertically.

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It reflects the graph across the x-axis.

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What is the effect of shifting a function vertically?

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Shifting a function vertically moves the graph up or down without affecting its shape.

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