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^(-1)x. the range is -π/2,π/2 (type your answer in interval notation. simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.) state whether the function is continuous. select the correct choice and, if necessary, fill in the answer box to complete your choice. a. there is a point of discontinuity at x= (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. the function is continuous. determine increasing or decreasing behavior. select the correct choice and, if necessary, fill in the answer boxes to complete your choice. a. the function is increasing on the interval and decreasing on the interval (type your answers in interval notation. use a comma to separate answers as needed.) b. the function is always increasing. c. the function is always decreasing.

analyze the function for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. f(x)=sin^(-1)x. the range is -π/2,π/2 (type your answer in interval notation. simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.) state whether the function is continuous. select the correct choice and, if necessary, fill in the answer box to complete your choice. a. there is a point of discontinuity at x= (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. the function is continuous. determine increasing or decreasing behavior. select the correct choice and, if necessary, fill in the answer boxes to complete your choice. a. the function is increasing on the interval and decreasing on the interval (type your answers in interval notation. use a comma to separate answers as needed.) b. the function is always increasing. c. the function is always decreasing.

Answer

Explanation:

Step1: Determine domain

The domain of $y = \sin^{-1}x$ is $[-1,1]$ because the sine - function has values between $- 1$ and $1$, and the inverse - sine function is the inverse of the restricted sine function.

Step2: Recall range

The range of $y=\sin^{-1}x$ is $\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$.

Step3: Check continuity

The inverse - sine function $y = \sin^{-1}x$ is continuous on its domain $[-1,1]$.

Step4: Analyze increasing/decreasing behavior

The derivative of $y=\sin^{-1}x$ is $y'=\frac{1}{\sqrt{1 - x^{2}}}$, and for $x\in(-1,1)$, $y'>0$. So the function is always increasing on its domain $[-1,1]$.

Answer:

Domain: $[-1,1]$ Range: $\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$ Continuity: B. The function is continuous. Increasing/Decreasing: B. The function is always increasing.