
Vertical Asymptotes, Horizontal Asymptotes, & Holes
Flashcard
•
Mathematics
•
11th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a vertical asymptote?
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
What is a horizontal asymptote?
Back
A horizontal asymptote is a line y = b that a function approaches as x approaches infinity or negative infinity. It indicates the behavior of the function at extreme values of x.
3.
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.
4.
FLASHCARD QUESTION
Front
How do you find horizontal asymptotes in a rational function?
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 they are equal, divide the leading coefficients. 3) If the degree of the numerator is greater, there is no horizontal asymptote.
5.
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 equal zero. It indicates that the function is not defined at that point, but the limit exists.
6.
FLASHCARD QUESTION
Front
Given the function f(x) = (x^2 - 1)/(x - 1), identify the hole.
Back
The hole is at x = 1, because both the numerator and denominator equal zero at that point.
7.
FLASHCARD QUESTION
Front
What is the significance of identifying asymptotes in graphing functions?
Back
Identifying asymptotes helps in understanding the behavior of the function as it approaches certain values, guiding the sketching of the graph and indicating limits.
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