Answered

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2. Which of the following statements are true about the graph of f(x) = sec x? (Select all that apply)(0,1) is a point on the graph.f(x) is defined for all x.There is a vertical asymptote at x = /2.f(x) is undefined when sin x = 0.All x-values are included in the domain.

Sagot :

.The function f is given by:

[tex]f(x)=\sec(x)[/tex][tex]\begin{gathered} f(\frac{\pi}{3})=2 \\ f(\frac{\pi}{2})=\frac{1}{0} \\ f(0)=1 \\ f(\frac{\pi}{4})=\sqrt{2} \\ \end{gathered}[/tex]

[tex]\text{ Since }\cos(x)=0\text{ at }x=\frac{\pi}{2},\text{ it follows that the function }f\text{ has a vertical asymptote at }\frac{\pi}{2}[/tex]

Since f(0) = 1, it follows tha (0, 1) is on the line.

Hence, the correct answers are:

(0,1) is a point on the graph.

There is a vertical asymptote at x = /2.

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