Reciprocal Graphs

Reciprocal Graphs

Sketch and hence find the reciprocal graph

y = 0y = 1y = 2y = 1/2y = 3y = 1/3x = 1y = 0

HyperbolaAsymptoteAsymptoteDomain:x R\{1}

Range:y R\{0}

Asymptotes:x = 1y = 0

y-intercepty = 1

Reciprocal GraphsAll 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 pointsWhere y-value > 1, reciprocal < 1Where y-value < 1, reciprocal > 1Where original graph is negative, reciprocal is also negativeA 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 asymptotesGraphs should approach but not touch asymptotes and they should not curl away from asymptotes.State domain, range, equations of asymptotes, intercepts, turning points

Reciprocal Graphs (2)Sketch and hence find the reciprocal graph

y = 0x = 1x = 3

tp = (2, 1)Domain:x R\{1, 3}

Range:{y 1} {y > 0}

Asymptotes:y = 0x = 1x = 3

Stationary Point(2, 1) lcl max

Y-intercepty = 1/3