Asymptotes - PowerPoint PPT Presentation

Explore the concept of points of discontinuity in rational functions, where the denominator equals zero, leading to breaks in the graph. Learn about types of discontinuities such as vertical asymptotes and holes, and discover how to identify them in graphical representations through examples.

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Rational functions are expressed as the ratio of two polynomials. The domain of a rational function excludes values that make the denominator zero. Various examples illustrate how to determine the domain and identify asymptotes in rational functions. Vertical asymptotes exist where the denominator i

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Learn about rational functions, including how to define, simplify, and graph them. Explore the parts of graphs such as x-intercepts, y-intercepts, vertical asymptotes, horizontal asymptotes, angled asymptotes, and holes. Discover steps to find all information about rational functions, including hori

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The art of sketching graphs of functions involves representing specific shapes and behaviors through labeled diagrams. This lesson highlights key details to keep in mind when sketching functions, such as labeling axes, maximum and minimum values, intercepts, symmetry, and asymptotes. Two examples of

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Vertical and horizontal asymptotes play a crucial role in understanding the behavior of rational functions. Vertical asymptotes occur when the denominator of a rational function equals zero, leading to excluded values. On the other hand, horizontal asymptotes are determined by comparing the degrees

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This content discusses the characteristics and transformations of hyperbolas and circles, including their equations, graphs, asymptotes, and locator points. It explains standard forms and the impacts of h and k values on the functions. Explore the concepts with examples and detailed explanations.

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The reciprocal function, learn how to sketch it, identify domain and range, and find horizontal and vertical asymptotes. Explore the effects of changing constants on the graph.

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Rectangular hyperbolas are a type of hyperbola with perpendicular asymptotes. Learn about their characteristics, asymptotes, dilations, and reflections in this informative content. Explore how horizontal and vertical asymptotes guide the shape of these graphs.

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Graphs of the tangent and cotangent functions, their transformations, periods, domains, ranges, and asymptotes. Understand how to graph them using the unit circle, find vertical asymptotes, and apply vertical and horizontal shifts to the functions.

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