How can you identify a hole in a rational function from its equation?

To identify a hole in a rational function, factor both the numerator and denominator. If a common factor exists, the x-value that makes this factor zero indicates the location of the hole.

What is the difference between a hole and a vertical asymptote?

A hole indicates a point where the function is undefined due to a common factor in the numerator and denominator, while a vertical asymptote indicates a value where the function approaches infinity.

What is the general form of a rational function?

The general form of a rational function is $$f(x) = \frac{P(x)}{Q(x)}$$ , where P(x) and Q(x) are polynomials.

How do you graph a rational function?

To graph a rational function, identify holes, vertical asymptotes, horizontal asymptotes, and intercepts. Plot these key points and sketch the curve, considering the behavior near asymptotes.

What is the x-intercept of a rational function?

The x-intercept of a rational function occurs where the function equals zero, which is found by setting the numerator equal to zero and solving for x.

What is the y-intercept of a rational function?

The y-intercept of a rational function is found by evaluating the function at x = 0, i.e., $$f(0) = \frac{P(0)}{Q(0)}$$ , provided Q(0) is not zero.

What happens to the graph of a rational function as x approaches infinity?

As x approaches infinity, the graph of a rational function approaches its horizontal asymptote, indicating the end behavior of the function.

What is the domain of a rational function?

The domain of a rational function consists of all real numbers except for the values of x that make the denominator equal to zero.

rational functions graphs

Flashcard

•

Mathematics

•

10th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSF-IF.C.7D

Standards-aligned

Wayground Content

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FLASHCARD QUESTION

Front

What is a rational function?

Back

Tags

CCSS.HSF-IF.C.7D

FLASHCARD QUESTION

Front

What is a hole in a rational function graph?

Back

A hole in a rational function graph occurs at a value of x where both the numerator and denominator of the function equal zero, indicating that the function is undefined at that point.

Tags

CCSS.HSF-IF.C.7D

FLASHCARD QUESTION

Front

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

Back

The vertical asymptote of a rational function occurs at the values of x that make the denominator equal to zero, provided that these values do not also make the numerator zero.

Tags

CCSS.HSF-IF.C.7D

FLASHCARD QUESTION

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches infinity or negative infinity. It indicates the behavior of the function at extreme values.

Tags

CCSS.HSF-IF.C.7D

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSF-IF.C.7D

FLASHCARD QUESTION

Front

What is the significance of the leading coefficient in a rational function?

Back

The leading coefficient of the polynomial in the numerator or denominator affects the end behavior of the rational function, particularly in determining the horizontal asymptote.

Tags

CCSS.HSF-IF.C.7D

FLASHCARD QUESTION

Front

What does it mean if a rational function has a hole at x = -3?

Back

If a rational function has a hole at x = -3, it means that the function is undefined at this point, and the graph will not include the point ( -3, f(-3) ).

Tags

CCSS.HSF-IF.C.7D

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