How do you solve a rational equation?

To solve a rational equation, find a common denominator, eliminate the denominators, and then solve the resulting polynomial equation.

What is the significance of the y-intercept in a rational function?

The y-intercept indicates the value of the function when $$x=0$$ , providing insight into the function's behavior.

What is a hole in a rational function?

A hole occurs at a value of $$x$$ where both the numerator and denominator are zero, indicating a removable discontinuity.

How do you determine the end behavior of a rational function?

The end behavior can be determined by analyzing the leading coefficients and degrees of the numerator and denominator.

What is the difference between a removable and non-removable discontinuity?

A removable discontinuity occurs at a hole, while a non-removable discontinuity occurs at a vertical asymptote.

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

To find the x-intercepts, set the numerator equal to zero and solve for $$x$$ .

What is the importance of factoring in rational functions?

Factoring helps simplify rational functions, find intercepts, and identify asymptotes.

What is the relationship between the degrees of the numerator and denominator in determining horizontal asymptotes?

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is $$y=0$$ . If they are equal, the asymptote is $$y=\frac{a}{b}$$ where $$a$$ and $$b$$ are the leading coefficients.

Rational Functions Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is a rational function?

Back

Tags

CCSS.HSF-IF.C.7D

2.

FLASHCARD QUESTION

Front

What is the domain of a rational function?

Back

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

3.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSF-IF.C.7D

4.

FLASHCARD QUESTION

Front

What does it mean for a rational function to be undefined?

Back

Tags

CCSS.HSF-IF.C.7D

5.

FLASHCARD QUESTION

Front

How do you simplify a rational function?

Back

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

Tags

CCSS.HSA.APR.D.6

6.

FLASHCARD QUESTION

Front

What is the vertical asymptote of a rational function?

Back

Tags

CCSS.HSF-IF.C.7D

7.

FLASHCARD QUESTION

Front

What is the horizontal asymptote of a rational function?

Back

Tags

CCSS.HSF-IF.C.7D

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