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)=sin⁻¹x identify any local minima. select the correct choice and, if necessary, fill in the answer box to complete your choice. a. there is a minimum at x = -1 (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression. use a comma to separate answers as needed.) b. there are no local minima. identify any horizontal asymptotes. select the correct choice and, if necessary, fill in the answer box to complete your choice. a. 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.) b. 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.) c. the function has no horizontal asymptotes clear all

analyze the function for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. f(x)=sin⁻¹x identify any local minima. select the correct choice and, if necessary, fill in the answer box to complete your choice. a. there is a minimum at x = -1 (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression. use a comma to separate answers as needed.) b. there are no local minima. identify any horizontal asymptotes. select the correct choice and, if necessary, fill in the answer box to complete your choice. a. 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.) b. 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.) c. the function has no horizontal asymptotes clear all

Answer

Answer:

  1. Local minima:
    • A. There is a minimum at (x = - 1)
  2. Horizontal asymptotes:
    • C. The function has no horizontal asymptotes

Explanation:

Step1: Analyze local - minima of (y = \sin^{-1}x)

The domain of (y=\sin^{-1}x) is ([-1,1]) and its derivative (y'=\frac{1}{\sqrt{1 - x^{2}}}). The function (y = \sin^{-1}x) is increasing on its domain ([-1,1]). So, the minimum value occurs at (x=-1) and (\sin^{-1}(-1)=-\frac{\pi}{2}).

Step2: Analyze horizontal asymptotes of (y = \sin^{-1}x)

The domain of (y=\sin^{-1}x) is ([-1,1]). Since the function is only defined for (x\in[-1,1]), as (x\to\pm\infty), the function is not defined. So, there are no horizontal asymptotes.