
Understanding Asymptotes and Holes
Flashcard
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Hard
Standards-aligned
Wayground Content
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15 questions
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1.
FLASHCARD QUESTION
Front
What is an asymptote?
Back
An asymptote is a line that a graph approaches but never touches. It can be vertical, horizontal, or slant.
Tags
CCSS.HSF-IF.C.7D
2.
FLASHCARD QUESTION
Front
What is a hole in a graph?
Back
A hole occurs in a graph at a point where a function is not defined due to a factor that cancels out in the function's expression.
Tags
CCSS.HSF-IF.C.7D
3.
FLASHCARD QUESTION
Front
How do you find the slant asymptote of a rational function?
Back
To find the slant asymptote, perform polynomial long division on the numerator by the denominator. The quotient (ignoring the remainder) gives the equation of the slant asymptote.
Tags
CCSS.HSF-IF.C.7D
4.
FLASHCARD QUESTION
Front
What is the horizontal asymptote of a rational function?
Back
The horizontal asymptote is determined by 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, it is y=ratio of leading coefficients.
Tags
CCSS.HSF-IF.C.7D
5.
FLASHCARD QUESTION
Front
How do you determine x-intercepts of a function?
Back
To find x-intercepts, set the numerator of the rational function equal to zero and solve for x.
Tags
CCSS.HSF-IF.C.7D
6.
FLASHCARD QUESTION
Front
What is the domain of a rational function?
Back
The domain consists of all real numbers except where the denominator equals zero.
7.
FLASHCARD QUESTION
Front
What is the range of a rational function?
Back
The range includes all real numbers except for any horizontal asymptotes or holes in the graph.
Tags
CCSS.HSF-IF.C.7D
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