graph the following function. show at least two cycles. use the graph to determine the domain and range of…

graph the following function. show at least two cycles. use the graph to determine the domain and range of the function.\ny = 3 sec x\nuse the graph to determine the domain of y = 3 sec x.\na. all real numbers\nb. {x|x ≠ kπ, k is an integer}\nc. {x|x ≠ \\frac{kπ}{2}, k is an odd integer}\nd. {x|x ≠ \\frac{kπ}{4}, k is an odd integer}\nuse the graph to determine the range of y = 3 sec x.\nthe range is □.

graph the following function. show at least two cycles. use the graph to determine the domain and range of the function.\ny = 3 sec x\nuse the graph to determine the domain of y = 3 sec x.\na. all real numbers\nb. {x|x ≠ kπ, k is an integer}\nc. {x|x ≠ \\frac{kπ}{2}, k is an odd integer}\nd. {x|x ≠ \\frac{kπ}{4}, k is an odd integer}\nuse the graph to determine the range of y = 3 sec x.\nthe range is □.

Answer

Explanation:

Step1: Recall the definition of secant function

The function (y = 3\sec x=\frac{3}{\cos x}). The cosine function (\cos x = 0) when (x=\frac{k\pi}{2}), (k) is an odd integer. Since the function (y = 3\sec x) is undefined when (\cos x = 0), the domain of (y = 3\sec x) is (\left{x|x\neq\frac{k\pi}{2},k\text{ is an odd integer}\right}).

Step2: Analyze the range of the secant function

We know that (- 1\leqslant\cos x\leqslant1). When (\cos x) is positive, (\cos x\in(0,1]), then (y = 3\sec x=\frac{3}{\cos x}\geqslant3). When (\cos x) is negative, (\cos x\in[- 1,0)), then (y = 3\sec x=\frac{3}{\cos x}\leqslant - 3).

Answer:

For the domain: C. (\left{x|x\neq\frac{k\pi}{2},k\text{ is an odd integer}\right}) For the range: ((-\infty,-3]\cup[3,\infty))