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)=tan^(-1)x b. 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.) c. the function has no vertical asymptotes. describe the end behavior. select the correct choice and, if necessary, fill in the answer boxes to complete your choice. a. the function approaches as x approaches positive infinity and the function approaches as x approaches negative infinity. (simplify your answers. type exact answers, using π as needed. use integers or fractions for any numbers in the expressions.) b. the domain is bounded and the function has no end behavior.

analyze the function for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. f(x)=tan^(-1)x b. 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.) c. the function has no vertical asymptotes. describe the end behavior. select the correct choice and, if necessary, fill in the answer boxes to complete your choice. a. the function approaches as x approaches positive infinity and the function approaches as x approaches negative infinity. (simplify your answers. type exact answers, using π as needed. use integers or fractions for any numbers in the expressions.) b. the domain is bounded and the function has no end behavior.

Answer

Explanation:

Step1: Recall domain and range of inverse - tangent

The domain of $y = \tan^{-1}x$ is $(-\infty,\infty)$ and the range is $(-\frac{\pi}{2},\frac{\pi}{2})$.

Step2: Check for vertical asymptotes

Since the domain of $y=\tan^{-1}x$ is all real numbers, there are no vertical asymptotes.

Step3: Analyze end - behavior

As $x\rightarrow+\infty$, $\tan^{-1}x\rightarrow\frac{\pi}{2}$ and as $x\rightarrow-\infty$, $\tan^{-1}x\rightarrow-\frac{\pi}{2}$.

Answer:

For the vertical asymptotes question: C. The function has no vertical asymptotes. For the end - behavior question: A. The function approaches $\frac{\pi}{2}$ as $x$ approaches positive infinity and the function approaches $-\frac{\pi}{2}$ as $x$ approaches negative infinity.