Asymptotes definitions Flashcards
Asymptotes definitions
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Asymptote
A line that a graph approaches infinitely closely but never touches, shaping the behavior of rational functions. Rational Function
A function expressed as the ratio of two polynomials, often exhibiting asymptotic behavior. Horizontal Asymptote
A horizontal line indicating the value a function approaches as x moves toward positive or negative infinity. Vertical Asymptote
A vertical line where a function's value increases or decreases without bound as x approaches a specific value. End Behavior
The trend of a graph as x approaches infinity or negative infinity, often influenced by asymptotes. Lowest Terms
A simplified form of a rational function where all common factors between numerator and denominator are canceled. Common Factor
An expression that divides both the numerator and denominator, whose cancellation may create a hole in the graph. Hole
A point of discontinuity on a graph, marked by an open circle, resulting from a canceled common factor. Removable Discontinuity
A technical term for a hole in a graph, occurring where a common factor is canceled from a rational function. Domain
The set of all possible input values for a function, restricted by vertical asymptotes and holes. Range
The set of all possible output values for a function, often influenced by horizontal asymptotes. Degree
The highest exponent of a variable in a polynomial, used to determine the presence and location of horizontal asymptotes. Leading Coefficient
The coefficient of the term with the highest degree in a polynomial, used to find horizontal asymptotes when degrees are equal. Dashed Line
A graphical representation used to indicate the location of an asymptote on a coordinate plane. Removable Factor
A factor that, when canceled from both numerator and denominator, creates a hole rather than an asymptote.
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