Asymptotes definitions Flashcards
Asymptotes definitions
You can tap to flip the card.
Control buttons has been changed to "navigation" mode.
1/15Skip to main content
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.
6:24
