4. Graphing Trigonometric Functions

Match each function with its graph in choices A - D.

y = sec (x - π/2)

Match each function with its graph in choices A–F.

y = tan (x - π )

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In Exercises 25–28, use each graph to obtain the graph of the corresponding reciprocal function, cosecant or secant. Give the equation of the function for the graph that you obtain.

In Exercises 29–44, graph two periods of the given cosecant or secant function. y = 2 sec x

In Exercises 29–44, graph two periods of the given cosecant or secant function. y = sec x/3

In Exercises 29–44, graph two periods of the given cosecant or secant function. y = −2 csc πx

In Exercises 29–44, graph two periods of the given cosecant or secant function. y = −1/2 sec πx

In Exercises 29–44, graph two periods of the given cosecant or secant function. y = csc(x − π)

In Exercises 29–44, graph two periods of the given cosecant or secant function. y = 2 sec(x + π)

In Exercises 45–52, graph two periods of each function. y = sec(2x + π/2) − 1

In Exercises 45–52, graph two periods of each function. y = csc|x|

In Exercises 53–54, let f(x) = 2 sec x, g(x) = −2 tan x, and h(x) = 2x − π/2. Graph two periods of y = (f∘h)(x).

In Exercises 17–24, graph two periods of the given cotangent function. y = 1/2 cot 2x

In Exercises 18–24, graph two full periods of the given tangent or cotangent function. y = −2 tan π/4 x