Steps in Graphing a Transformation of a Cosecant Function
1) Do you know the shape of the final graph? (Is it a reflection of cosecant or not?) 2) Do you know the length of the period? (2pi/b=period) 3) Do you know the phase shift? (-c/b = phase shift) 4) Do you know THREE of the asymptotes? solve 0 =bx+c and pi=bx+c and 2pi=bx+c 5) Do you know ALL of the asymptotes? x = asymptote +1/2period*n with n being an integer 4) Can you find two points that lie on the intended graph of the transformation? 5) Do you know where the midline is? (y = d) 6) Do you know what the sign of a tells you about the location of the points of the graph of the transformation? (Is a is negative? Where do the special points live on the graph?)
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