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\na. 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.)\nb. 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.)\nc. the function has no horizontal asymptotes.\nidentify any vertical asymptotes. select the correct choice and, if necessary, fill in the answer box to complete your choice.\na. the function has one vertical 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.)\nb. the function has two vertical asymptotes. the leftmost asymptote is and the rightmost asymptote is (type equations. simplify your answers. type exact answers, using π as needed. use integers or fractions for any numbers in the equations.)\nc. the function has no vertical asymptotes.

analyze the function for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior f(x)=sin⁻¹x\na. 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.)\nb. 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.)\nc. the function has no horizontal asymptotes.\nidentify any vertical asymptotes. select the correct choice and, if necessary, fill in the answer box to complete your choice.\na. the function has one vertical 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.)\nb. the function has two vertical asymptotes. the leftmost asymptote is and the rightmost asymptote is (type equations. simplify your answers. type exact answers, using π as needed. use integers or fractions for any numbers in the equations.)\nc. the function has no vertical asymptotes.

Answer

Answer:

  1. C. The function has no horizontal asymptotes.
  2. C. The function has no vertical asymptotes.

Explanation:

Step1: Recall domain and range of inverse - sine function

The domain of (y = \sin^{-1}(x)) is ([- 1,1]) and the range is (\left[-\frac{\pi}{2},\frac{\pi}{2}\right]). Since the function is defined on a closed - interval ([-1,1]), as (x\to\pm\infty), the function is not defined, so there are no horizontal asymptotes.

Step2: Analyze vertical asymptotes

For a vertical asymptote, the function must approach (\pm\infty) as (x) approaches a certain value. The inverse - sine function (y=\sin^{-1}(x)) is well - defined and continuous on its domain ([-1,1]). There are no values of (x) within the domain or approaching the domain boundaries for which the function approaches (\pm\infty), so there are no vertical asymptotes.