What does it mean if a rational function has no horizontal asymptote?

It means that as $$x$$ approaches infinity or negative infinity, the function does not approach a constant value.

Identify the vertical asymptote of $$f(x) = \frac{2}{x-5}$$ .

The vertical asymptote is $$x = 5$$ .

Subtract $$\frac{6}{x-1}-\frac{5x}{4}$$ .

The result is $$\frac{-5x^2+5x+24}{4(x-1)}$$ .

What is the significance of the leading coefficient in determining horizontal asymptotes?

The leading coefficient of the numerator and denominator helps determine the horizontal asymptote when their degrees are equal.

What happens to the graph of a rational function at its vertical asymptotes?

The graph approaches the vertical asymptote but never touches or crosses it.

Explain the concept of holes in rational functions.

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

What is the domain of a rational function?

The domain of a rational function includes all real numbers except those that make the denominator zero.

How do you simplify a rational function?

To simplify a rational function, factor both the numerator and denominator and cancel any common factors.

Rational Functions & Equations Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

Define 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.

2.

FLASHCARD QUESTION

Front

What is the general form of a rational function?

Back

3.

FLASHCARD QUESTION

Front

What is a vertical asymptote?

Back

4.

FLASHCARD QUESTION

Front

How do you find vertical asymptotes of a rational function?

Back

5.

FLASHCARD QUESTION

Front

What is a horizontal asymptote?

Back

6.

FLASHCARD QUESTION

Front

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

Back

7.

FLASHCARD QUESTION

Front

Back

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