Graphing Rational Functions definitions Flashcards
Graphing Rational Functions definitions
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Rational Function An expression formed by dividing one polynomial by another, often exhibiting asymptotes and restricted domains. Transformation A change applied to a graph, such as shifting, reflecting, or stretching, altering its position or orientation. Vertical Asymptote A dashed line where the graph approaches but never touches, occurring where the denominator equals zero. Horizontal Asymptote A dashed line indicating the value a function approaches as x becomes very large or very small. Reflection A flip of the graph over the x-axis or y-axis, determined by a negative sign outside or inside the function. Horizontal Shift A movement of the graph left or right, determined by the value subtracted from x inside the function. Vertical Shift A movement of the graph up or down, determined by a constant added or subtracted outside the function. Domain All possible x-values for which the function is defined, often excluding values that make the denominator zero. Range All possible y-values the function can take, typically split by horizontal asymptotes. X-intercept A point where the graph crosses the x-axis, found by setting the numerator equal to zero. Y-intercept A point where the graph crosses the y-axis, found by evaluating the function at x equals zero. Multiplicity The number of times a factor appears in the numerator or denominator, affecting how the graph behaves at intercepts. Interval A section of the x-axis between key points like asymptotes or intercepts, used to analyze graph behavior. Set Notation A mathematical way to describe domain and range, often using symbols like parentheses and union. Leading Coefficient The coefficient of the highest degree term in a polynomial, used to determine horizontal asymptotes.
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