A line that a rational function graph approaches infinitely close but never touches, shaping the graph's behavior at extremes or near undefined points.
Rational Function
A function expressed as the ratio of two polynomials, often exhibiting unique features like asymptotes and holes.
Horizontal Asymptote
A horizontal line indicating the y-value a rational function approaches as x moves toward positive or negative infinity.
Vertical Asymptote
A vertical line where a rational function becomes undefined, causing the graph to shoot up or down without bound near specific x-values.
Hole
A point of discontinuity on a rational function's graph, marked by an open circle, resulting from a canceled common factor.
Removable Discontinuity
A gap in a rational function's graph at a specific x-value, caused by a factor that cancels from both numerator and denominator.
Domain
The set of all possible x-values for which a rational function is defined, excluding values causing division by zero.
Range
The set of all possible y-values a rational function can output, influenced by horizontal asymptotes and holes.
Leading Coefficient
The coefficient of the term with the highest degree in a polynomial, crucial for determining horizontal asymptotes.
Degree
The highest exponent of the variable in a polynomial, used to compare numerator and denominator for asymptote analysis.
Lowest Terms
A simplified form of a rational function where all common factors between numerator and denominator are canceled.
Dashed Line
A graphical representation used to indicate the location of an asymptote on a rational function's graph.
End Behavior
The trend of a rational function's graph as x approaches infinity or negative infinity, often dictated by horizontal asymptotes.
Common Factor
A polynomial expression present in both the numerator and denominator, whose cancellation may create a hole.
Arrow Notation
A symbolic way to describe how a function behaves as x approaches certain values, especially near asymptotes.