Consider the function f(x)=arctan [(x+6)/(x+5)] Express thedomain of the function in interval notation: Find the y-intercept:y= . Find all the x-intercepts (enter your answer as acomma-separated list): x= . Does f have any symmetries? f is even;f is odd; f is periodic; None of the above. Find all the asymptotesof f (enter your answers as comma-separated list; if the list isempty, enter DNE): Vertical asymptotes: ; Horizontal asymptotes: ;Slant asymptotes: . Determine the derivative of f. f'(x)= On whichintervals is f increasing/decreasing? (Use the union symbol and nota comma to separate different intervals; if the function is nowhereincreasing or nowhere decreasing, use DNE as appropriate). f isincreasing on . f is decreasing on . List all the local maxima andminima of f. Enter each maximum or minimum as the coordinates ofthe point on the graph. For example, if f has a maximum at x=3 andf(3)=9, enter (3,9) in the box for maxima. If there are multiplemaxima or minima, enter them as a comma-separated list of points,e.g. (3,9),(0,0),(4,7) . If there are none, enter DNE. Localmaxima: . Local minima: . Determine the second derivative of f.f''(x)= On which intervals does f have concavity upwards/downwards?(Use the union symbol and not a comma to separate differentintervals; if the function does not have concavity upwards ordownwards on any interval, use DNE as appropriate). f is concaveupwards on . f is concave downwards on . List all the inflectionpoints of f. Enter each inflection point as the coordinates of thepoint on the graph. For example, if f has an inflection point atx=7 and f(7)=?2, enter (7,?2) in the box. If there are multipleinflection points, enter them as a comma-separated list, e.g.(7,?2),(0,0),(4,7) . If there are none, enter DNE. Does thefunction have any of the following features? Select all that apply.Removable discontinuities (i.e. points where the limit exists, butit is different than the value of the function) Corners (i.e.points where the left and right derivatives are defined but aredifferent) Jump discontinuities (i.e. points where the left andright limits exist but are different) Points with a verticaltangent line Upload a sketch of the graph of f. You can use a pieceof paper and a scanner or a camera, or you can use a tablet, butthe sketch must be drawn by hand. You should include all relevantinformation that has not been requested here, for example thelimits at the edges of the domain and the slopes of tangent linesat interesting points (e.g. inflection points). Make sure that thepicture is clear, legible, and correctly oriented.