Rational Functions Transformations and Characteristics

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What are the x-intercepts of the function?

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The x-intercepts are the points where the graph crosses the x-axis. For the given function, the x-intercepts are x = 4 and x = -2.

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How do you find the x-intercept of a rational function?

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To find the x-intercept, replace the y-value with 0 or make the numerator equal to 0.

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What is a horizontal asymptote?

Back

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

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What is the horizontal asymptote of the function if the degrees of the numerator and denominator are equal?

Back

If the degrees of the numerator and denominator are equal, the horizontal asymptote is given by the ratio of the leading coefficients.

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What is the horizontal asymptote of the function if the degree of the numerator is less than the degree of the denominator?

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If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0.

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What is the horizontal asymptote of the function if the degree of the numerator is greater than the degree of the denominator?

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If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

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In the function, 'a' represents the vertical stretch or compression factor.

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In the function, 'h' represents the horizontal shift of the graph.

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In the function, 'k' represents the vertical shift of the graph.

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The range of the function is all real numbers except y = 2.