What is a vertical asymptote?
Horizontal/Vertical Asymptotoes/Holes

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•
Mathematics
•
11th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as x approaches a. It occurs when the denominator of a rational function equals zero and the numerator does not equal zero at that point.
2.
FLASHCARD QUESTION
Front
How do you find vertical asymptotes in a rational function?
Back
To find vertical asymptotes, set the denominator of the rational function equal to zero and solve for x. The values of x that make the denominator zero are the vertical asymptotes, provided the numerator is not also zero at those points.
3.
FLASHCARD QUESTION
Front
What is a hole in a function?
Back
A hole occurs in a function at a point where both the numerator and denominator are zero, indicating that the function is not defined at that point, but the limit exists.
4.
FLASHCARD QUESTION
Front
How do you identify holes in a rational function?
Back
To identify holes, factor both the numerator and denominator. If a common factor exists, set it equal to zero to find the x-coordinate of the hole.
5.
FLASHCARD QUESTION
Front
What is a horizontal asymptote?
Back
A horizontal asymptote is a line y = b where a function approaches the value b as x approaches infinity or negative infinity. It describes the end behavior of the function.
6.
FLASHCARD QUESTION
Front
How do you find horizontal asymptotes in rational functions?
Back
To find horizontal asymptotes, compare the degrees of the numerator and denominator: 1) If the degree of the numerator is less than the degree of the denominator, y = 0 is the horizontal asymptote. 2) If the degrees are equal, divide the leading coefficients. 3) If the degree of the numerator is greater, there is no horizontal asymptote.
7.
FLASHCARD QUESTION
Front
What is the significance of the degree of the numerator and denominator in determining horizontal asymptotes?
Back
The degree of the numerator and denominator determines the end behavior of the function. It helps identify whether the function approaches a specific value (horizontal asymptote) or diverges (no horizontal asymptote).
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