What is the horizontal asymptote of $$f(x) = \frac{2x^2 + 3}{x^2 + 1}$$ ?

The horizontal asymptote is $$y = 2$$ because the degrees of the numerator and denominator are the same.

What is the vertical asymptote of $$f(x) = \frac{1}{x-3}$$ ?

The vertical asymptote is $$x = 3$$ .

What is the significance of horizontal asymptotes in graphing?

Horizontal asymptotes indicate the end behavior of a function as x approaches infinity or negative infinity.

What is the horizontal asymptote of $$f(x) = \frac{3x + 1}{2}$$ ?

The horizontal asymptote is $$y = \frac{3}{2}$$ .

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

If a function has no horizontal asymptote, it means that as x approaches infinity or negative infinity, the function's value continues to increase or decrease without bound.

What is the horizontal asymptote of $$f(x) = \frac{x^3}{x^2 + 1}$$ ?

The horizontal asymptote is $$y = \infty$$ , indicating that the function does not approach a finite value.

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 $$y = \frac{leading coefficient of numerator}{leading coefficient of denominator}$$ .

What is an example of a function with a vertical asymptote?

An example is $$f(x) = \frac{1}{x^2 - 4}$$ , which has vertical asymptotes at $$x = 2$$ and $$x = -2$$ .

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

A vertical asymptote indicates that the function approaches infinity, while a hole occurs when both the numerator and denominator are zero at the same x-value, indicating a removable discontinuity.

How can you identify asymptotes from a graph?

Asymptotes can be identified by looking for lines that the graph approaches but does not cross, as well as points where the graph becomes undefined.

Asymptotes Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches. It can be horizontal, vertical, or oblique.

Tags

CCSS.HSF-IF.C.7D

2.

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 positive or negative infinity.

Tags

CCSS.HSF-IF.C.7D

3.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSF-IF.C.7D

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7D

5.

FLASHCARD QUESTION

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line that the graph of a function approaches as the function's value approaches infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

6.

FLASHCARD QUESTION

Front

How do you find vertical asymptotes?

Back

Vertical asymptotes occur at values of x that make the denominator of a rational function equal to zero, provided the numerator is not also zero at those points.

Tags

CCSS.HSF-IF.C.7D

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7D

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