Reciprocal Graphs

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

2. 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, reciprocal > 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

3. Reciprocal Graphs (2) Sketch and hence find the reciprocal graph 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 y = 0 tp = (2, 1) x = 3 x = 1