Horizontal and Vertical Asymptotes

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•
Mathematics
•
10th - 12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a horizontal asymptote?
Back
A horizontal asymptote is a horizontal line that the graph of a function approaches as the input (x) approaches positive or negative infinity.
2.
FLASHCARD QUESTION
Front
How do you find the horizontal asymptote of a rational function?
Back
To find the horizontal asymptote of a rational function, compare the degrees of the numerator and denominator. 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 = leading coefficient of numerator / leading coefficient of denominator.
3.
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 input (x) approaches a certain value, typically where the function is undefined.
4.
FLASHCARD QUESTION
Front
How do you find vertical asymptotes in a rational function?
Back
Vertical asymptotes can be found by setting the denominator of a rational function equal to zero and solving for x.
5.
FLASHCARD QUESTION
Front
What does it mean if a function has no horizontal asymptote?
Back
If a function has no horizontal asymptote, it means that as x approaches positive or negative infinity, the function does not approach a specific y-value.
6.
FLASHCARD QUESTION
Front
What is the significance of the horizontal asymptote y=4?
Back
The horizontal asymptote y=4 indicates that as x approaches positive or negative infinity, the function's output approaches 4.
7.
FLASHCARD QUESTION
Front
What does the vertical asymptote x=2 indicate?
Back
The vertical asymptote x=2 indicates that the function approaches infinity or negative infinity as x approaches 2 from either side.
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