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Reciprocal Graphs Sketch and hence find the reciprocal graph y = 0 y = 1 y = 2 y = 1/2 y = 3 y = 1/3 x = 1 y = 0 Hyperbola Asymptote Domain: x R\{1} Range: y R\{0} Asymptotes: x = 1 y = 0 y-intercept y = 1

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Reciprocal Graphs All reciprocal graphs have a horizontal asymptote along the x-axis (y = 0) Where the original graph has an x-intercept (y-value = 0), there will be a vertical asymptote. (Draw in and label) Where y-value = 1 (or 1), the reciprocal is also 1 (or 1), so the graph and its reciprocal will intersect at those points Where y-value > 1, reciprocal < 1 Where y-value 1 Where original graph is negative, reciprocal is also negative A turning point not on the x-axis will create a turning point at the same x- coordinate in the reciprocal graph. Pay attention to each end of x-axis and close to vertical asymptotes Graphs should approach but not touch asymptotes and they should not curl away from asymptotes. State domain, range, equations of asymptotes, intercepts, turning points

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Reciprocal Graphs (2) Sketch and hence find the reciprocal graph y = 0 x = 1 x = 3 tp = (2, 1) Domain: x R\{1, 3} Range: {y 1} {y > 0} Asymptotes: y = 0 x = 1 x = 3 Stationary Point (2, 1) lcl max Y-intercept y = 1/3