Consider the function f(x)=arctan [(x+6)/(x+5)]
Express the domain of the function in interval notation: Findthe y-intercept: y= . Find all the x-intercepts (enter your answeras a comma-separated list): x= . Does f have any symmetries? f iseven; f is odd; f is periodic; None of the above. Find all theasymptotes of f (enter your answers as comma-separated list; if thelist is empty, enter DNE): Vertical asymptotes: ; Horizontalasymptotes: ; Slant asymptotes: . Determine the derivative of f.f'(x)= On which intervals is f increasing/decreasing? (Use theunion symbol and not a comma to separate different intervals; ifthe function is nowhere increasing or nowhere decreasing, use DNEas appropriate). f is increasing on . f is decreasing on . List allthe local maxima and minima of f. Enter each maximum or minimum asthe coordinates of the point on the graph. For example, if f has amaximum at x=3 and f(3)=9, enter (3,9) in the box for maxima. Ifthere are multiple maxima or minima, enter them as acomma-separated list of points, e.g. (3,9),(0,0),(4,7) . If thereare none, enter DNE. Local maxima: . Local minima: . Determine thesecond derivative of f. f''(x)= On which intervals does f haveconcavity upwards/downwards? (Use the union symbol and not a commato separate different intervals; if the function does not haveconcavity upwards or downwards on any interval, use DNE asappropriate). f is concave upwards on . f is concave downwards on .List all the inflection points of f. Enter each inflection point asthe coordinates of the point on the graph. For example, if f has aninflection point at x=7 and f(7)=−2, enter (7,−2) in the box. Ifthere are multiple inflection points, enter them as acomma-separated list, e.g. (7,−2),(0,0),(4,7) . If there are none,enter DNE.
Does the function have any of the following features? Select allthat apply.
Removable discontinuities (i.e. points where the limit exists,but it is different than the value of the function)
Corners (i.e. points where the left and right derivatives aredefined but are different)
Jump discontinuities (i.e. points where the left and rightlimits exist but are different)
Points with a vertical tangent line
Upload a sketch of the graph of f. You can use a piece of paperand a scanner or a camera, or you can use a tablet, but the sketchmust be drawn by hand. You should include all relevant informationthat has not been requested here, for example the limits at theedges of the domain and the slopes of tangent lines at interestingpoints (e.g. inflection points). Make sure that the picture isclear, legible, and correctly oriented.
