analyze the function for domain, range, continuity, increasing or decreasing behavior, symmetry…

analyze the function for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. f(x)=cos^(-1)x identify any horizontal asymptotes. select the correct choice and, if necessary, fill in the answer box to complete your choice. o a. the function has one horizontal asymptote at. (type an equation. simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the equation.) o b. the function has two horizontal asymptotes. the top asymptote is and the bottom asymptote is. (type equations. simplify your answers. type exact answers, using π as needed. use integers or fractions for any numbers in the equations.) o c. the function has no horizontal asymptotes. identify any vertical asymptotes. select the correct choice and, if necessary, fill in the answer box to complete your choice.

analyze the function for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. f(x)=cos^(-1)x identify any horizontal asymptotes. select the correct choice and, if necessary, fill in the answer box to complete your choice. o a. the function has one horizontal asymptote at. (type an equation. simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the equation.) o b. the function has two horizontal asymptotes. the top asymptote is and the bottom asymptote is. (type equations. simplify your answers. type exact answers, using π as needed. use integers or fractions for any numbers in the equations.) o c. the function has no horizontal asymptotes. identify any vertical asymptotes. select the correct choice and, if necessary, fill in the answer box to complete your choice.

Answer

Explanation:

Step1: Recall domain and range of inverse - cosine function

The domain of (y = \cos^{-1}x) is ([- 1,1]) and the range is ([0,\pi]).

Step2: Analyze continuity

The inverse - cosine function (y=\cos^{-1}x) is continuous on its domain ([-1,1]).

Step3: Analyze increasing/decreasing behavior

The function (y = \cos^{-1}x) is a decreasing function on its domain ([-1,1]) since if (x_1<x_2) where (x_1,x_2\in[-1,1]), then (\cos^{-1}(x_1)>\cos^{-1}(x_2)).

Step4: Analyze symmetry

The function (y = \cos^{-1}x) has no symmetry about the (y) - axis or the origin.

Step5: Analyze boundedness

The function (y=\cos^{-1}x) is bounded. It is bounded below by (y = 0) and bounded above by (y=\pi).

Step6: Analyze extrema

The maximum value of (y=\cos^{-1}x) is (\pi) when (x=-1) and the minimum value is (0) when (x = 1).

Step7: Analyze asymptotes

The function (y=\cos^{-1}x) is defined only for (x\in[-1,1]). There are no horizontal asymptotes because the function is not defined for (|x|>1) and its range is a closed - interval ([0,\pi]). There are no vertical asymptotes since the function is continuous on its domain ([-1,1]).

Answer:

For horizontal asymptotes: C. The function has no horizontal asymptotes. For vertical asymptotes: C. The function has no vertical asymptotes.