Vertical and Horizontal Asymptotes

Flashcard
•
Mathematics
•
12th Grade
•
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 function is undefined at x = a.
2.
FLASHCARD QUESTION
Front
How do you find vertical asymptotes algebraically?
Back
To find vertical asymptotes, set the denominator of a rational function equal to zero and solve for x.
3.
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.
4.
FLASHCARD QUESTION
Front
How do you determine horizontal asymptotes for rational functions?
Back
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, y = leading coefficient of numerator / leading coefficient of denominator. 3. If the degree of the numerator is greater, there is no horizontal asymptote.
5.
FLASHCARD QUESTION
Front
Back
6.
FLASHCARD QUESTION
Front
What is the significance of asymptotes in graphing functions?
Back
Asymptotes help identify the behavior of a function as it approaches certain values, guiding the sketching of the graph.
7.
FLASHCARD QUESTION
Front
Back
x = 3 and x = -4.
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