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Magazine Problem 68
For the following exercises, sketch two periods of the graph for each of the following functions. Identify the stretching factor, period, and asymptotes. $$ h(x)=2 \sec \left(\frac{\pi}{4}(x+1)\right) $$
Problem 69
For the following exercises, sketch two periods of the graph for each of the following functions. Identify the stretching factor, period, and asymptotes. $$ m(x)=6 \csc \left(\frac{\pi}{3} x+\pi\right) $$
Problem 70
For the following exercises, sketch two periods of the graph for each of the following functions. Identify the stretching factor, period, and asymptotes. $$ j(x)=\tan \left(\frac{\pi}{2} x\right) $$
Problem 71
For the following exercises, sketch two periods of the graph for each of the following functions. Identify the stretching factor, period, and asymptotes. $$ p(x)=\tan \left(x-\frac{\pi}{2}\right) $$
Problem 72
For the following exercises, sketch two periods of the graph for each of the following functions. Identify the stretching factor, period, and asymptotes. $$ f(x)=4 \tan (x) $$
Problem 73
For the following exercises, sketch two periods of the graph for each of the following functions. Identify the stretching factor, period, and asymptotes. $$ f(x)=\tan \left(x+\frac{\pi}{4}\right) $$
Problem 74
For the following exercises, sketch two periods of the graph for each of the following functions. Identify the stretching factor, period, and asymptotes. $$ f(x)=\pi \tan (\pi x-\pi)-\pi $$
Problem 75
For the following exercises, sketch two periods of the graph for each of the following functions. Identify the stretching factor, period, and asymptotes. $$ f(x)=2 \csc (x) $$
Problem 76
For the following exercises, sketch two periods of the graph for each of the following functions. Identify the stretching factor, period, and asymptotes. $$ f(x)=-\frac{1}{4} \csc (x) $$
Problem 77
For the following exercises, sketch two periods of the graph for each of the following functions. Identify the stretching factor, period, and asymptotes. $$ f(x)=4 \sec (3 x) $$
