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Sketch Start with and then use addition of ordinates y = x + 5 +7 0.25 +6.75 +6 0.33 +5.67 +5 0.5 +4.5 +4 1.0 +3.0 Domain: x R\{2} Range: y R y-intercept: y = 4.5 x-intercepts: x = 1.70 x = 5.30 No stationary points Asymptotes x = 2 y = x + 5 1.7 5.3

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Graphing by Addition of Ordinates To draw a graph by addition of ordinates: 1. Sketch (using pencil or a light colour) the two original graphs 2. Draw in and label the asymptotes 3. For a variety of x-values, add the y-coordinates and mark the resultant points. Pay particular attention to: Values close to the vertical asymptotes Each end of the x-axis y-intercept placement of x-intercepts and turning points x-intercepts on the original graphs 4.Sketch the resultant graph by drawing a smooth curve through the points 5.Remember to take care drawing the graphs approaching asymptotes 6. Label graphs, axes, asymptotes, intercepts, turning points 7.State domain, range, intercepts and the equation of the asymptotes

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