8.1 Graph Rational Functions

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What is the DOMAIN of a rational function?

Back

The DOMAIN of a rational function is the set of all real numbers except where the denominator is zero.

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What is a vertical asymptote?

Back

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

Front

What is a horizontal asymptote?

Back

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

Front

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

Back

Set the denominator equal to zero and solve for x.

Front

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

Back

Compare the degrees of the numerator and denominator: If degree of numerator < degree of denominator, y = 0; If equal, y = leading coefficient of numerator/leading coefficient of denominator; If greater, no horizontal asymptote.

Front

What is the RANGE of a rational function?

Back

The RANGE of a rational function is the set of all possible output values (y-values) of the function.

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What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

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Back

The factored form is (x + 5)(x - 5).

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What is the significance of the vertical asymptote in graphing a rational function?

Back

The vertical asymptote indicates where the function is undefined and helps in understanding the behavior of the graph near that line.

Front

What is the significance of the horizontal asymptote in graphing a rational function?

Back

The horizontal asymptote indicates the value that the function approaches as x goes to infinity or negative infinity.