Rational Function Transformations

Front

What is a rational function?

Back

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

Front

What does it mean to transform a rational function?

Back

Transforming a rational function involves changing its position, shape, or size on a graph through operations such as shifting, stretching, or reflecting.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a rational function approaches infinity or negative infinity as x approaches a.

Front

How do you find vertical asymptotes of a rational function?

Back

Vertical asymptotes are found by setting the denominator of the rational function equal to zero and solving for x.

Front

What is a horizontal asymptote?

Back

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

Front

How do you determine horizontal asymptotes of a rational function?

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Horizontal asymptotes are determined by comparing the degrees of the numerator and denominator polynomials.

Front

What is a hole in a rational function?

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A hole occurs in a rational function at a value of x that makes both the numerator and denominator zero, indicating a removable discontinuity.

Front

What effect does a vertical shift have on a rational function?

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A vertical shift moves the graph of the rational function up or down by adding or subtracting a constant from the function.

Front

What effect does a horizontal shift have on a rational function?

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A horizontal shift moves the graph of the rational function left or right by adding or subtracting a constant from the variable x.

Front

What is a reflection in the context of rational functions?

Back

A reflection occurs when the graph of a rational function is flipped over a line, such as the x-axis or y-axis.