What is the slant asymptote of $$f(x) = \frac{4x^2 + 3x - 9}{x - 5}$$ ?

The slant asymptote is $$y = 4x + 23$$ .

Identify the slant asymptote of $$h(x) = \frac{2x^2 + 8x - 11}{x - 8}$$ .

The slant asymptote is $$y = 2x + 24$$ .

What is the slant asymptote for the function $$f(x) = \frac{x^2 - 4x + 2}{x + 3}$$ ?

The slant asymptote is $$y = x - 7$$ .

If a rational function has a degree of 3 in the numerator and 2 in the denominator, what type of asymptote can be expected?

The function will have a slant asymptote.

What is the slant asymptote for the function $$g(x) = \frac{3x^3 + 2x^2 - x + 1}{x^2 + 1}$$ ?

The slant asymptote is $$y = 3x$$ .

How can you determine if a function has a slant asymptote?

Check the degrees of the numerator and denominator. If the degree of the numerator is one more than the degree of the denominator, the function has a slant asymptote.

What is the formula for a slant asymptote derived from polynomial long division?

If $$f(x) = \frac{p(x)}{q(x)}$$ , the slant asymptote is given by the quotient of the division of $$p(x)$$ by $$q(x)$$ .

What is the slant asymptote of the function $$f(x) = \frac{5x^2 + 2x + 1}{x - 1}$$ ?

The slant asymptote is $$y = 5x + 7$$ .

Can a function have both a horizontal and a slant asymptote?

No, a function cannot have both a horizontal and a slant asymptote. If a function has a slant asymptote, it cannot have a horizontal asymptote.

What happens to the function as it approaches its slant asymptote?

As the function approaches its slant asymptote, the values of the function get closer to the values of the asymptote line, indicating that the function behaves similarly to the line at extreme values of x.

Provide an example of a function with a slant asymptote and state the asymptote.

Example: $$f(x) = \frac{x^2 + 3x + 2}{x + 1}$$ ; Slant asymptote: $$y = x + 2$$ .

Slant Asymptotes Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a slant asymptote?

Back

A slant asymptote (or oblique asymptote) is a line that a function approaches as the input (x) approaches infinity or negative infinity, typically occurring when the degree of the numerator is one higher than the degree of the denominator in a rational function.

Tags

CCSS.HSF-IF.C.7D

2.

FLASHCARD QUESTION

Front

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

Back

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CCSS.HSF-IF.C.7D

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7D

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7D

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7D

6.

FLASHCARD QUESTION

Front

What is the significance of slant asymptotes in graphing rational functions?

Back

Slant asymptotes help in understanding the end behavior of rational functions, indicating how the function behaves as x approaches infinity or negative infinity.

Tags

CCSS.HSF-IF.C.7D

7.

FLASHCARD QUESTION

Front

What is the difference between horizontal and slant asymptotes?

Back

Horizontal asymptotes occur when the degrees of the numerator and denominator are equal or the degree of the numerator is less than that of the denominator, while slant asymptotes occur when the degree of the numerator is exactly one more than that of the denominator.

Tags

CCSS.HSF-IF.C.7D

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