In this homework we will analyze the function f[:X:l s e-,rrl,."2 T ean:cat(x? l} Note: arccot (x? 1) is the power to which e is being raised. We will consider [0, 7] as the domain on which cot(x) is invertible. We want to use our calculus skills to create a decent graph of this complicated function. This homework will walk you through collecting relevant data. Then you'll use the data to draw your graph. Problem 1: Basic Information about f(x) (14 points) a) (2 points) What is the domain of f? (Give your answer in simplified interval notation.) b) (2 points) Is the function f(x) an odd function, and even function, or neither? Make sure you explain your answer. c) (2 points) Find any and all x-intercepts of f(x). d) (2 points) Find any and all y-intercepts of f(x). (Reminder: you are expected to evaluate any famous functions at standard values.) e) (2 points) Does f(x) have any vertical asymptotes? If so, give a formula for each vertical asymptote, and justify each vertical asymptote by evaluating a relevant limit. If there are no vertical asymptotes, explain how you know there are none