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 resulting in asymptotes and possible holes in its graph. Transformation A change applied to a graph, such as shifting, reflecting, or stretching, altering its position or orientation. Reflection A flip of a graph over a specific axis, caused by a negative sign inside or outside the function. Horizontal Shift A movement of a graph left or right, determined by the value subtracted or added to the input variable. Vertical Shift A movement of a graph up or down, determined by a constant added or subtracted outside the function. Vertical Asymptote A vertical dashed line on a graph where the function approaches infinity, found by setting the denominator to zero. Horizontal Asymptote A horizontal dashed line indicating the value a function approaches as x becomes very large or small. Domain The set of all possible input values for which a function is defined, often excluding values causing division by zero. Range The set of all possible output values a function can produce, often split by horizontal asymptotes. Set Notation A mathematical way to describe collections of numbers, often using unions and parentheses to indicate intervals. Hole A point where a function is undefined due to a common factor in the numerator and denominator, resulting in a gap in the graph. 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 zero. Multiplicity The number of times a factor appears in a polynomial, affecting whether a graph crosses or touches the axis at an intercept. Interval A section of the x-axis between known components like asymptotes and intercepts, used to analyze function behavior.
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