Question

Include all relevant work please.

s. Consider f(x) = *** a. Find the domain. [3] b. Find any vertical asymptotes. [3] c. Determine if there are any holes. If so, give the coordinates of the hole. [2] d. Find any horizontal or oblique asymptotes. [3] e. Determine if the graph intersects a horizontal/oblique asymptote, if it exists. Show work! [3] f. Sketch a graph of the function. To receive full credit, label any x and y intercepts and the asymptotes. If there is a hole in the graph, label it. 10 [5] - 10 -5 0 5 10 -5 -10

Answer 1

feals DC) 5) flats A-1 a) Domain of function is set of all possible values of dependent variable where function is defined Here flad is not defined for xs-5 so domain of fin) =R-453 6) A restical asymptotes for a function is a vertical line x=k where a fonction ten beomo unbounded of function is of the form a) whore Play qni are poly namical then for vestical Wymbores factor both numarator 4 denu mu'ator then reduced t sof dame meator a zero finding Vertical asyonpotes Now fials - 7 xts for retical asymbores ats=0 x = -5 c) Hole hole exists on the rational function at any Hallo of a that causes both the numer whor & denomicator. of the function to equal to be zewo. f for flere fals x-t at since there is no common the efor to those ů no holes. CS Scanned with CamScanner

d) A Horizontal asymptote for a function is a honžmful love that the graph of the function abbroaches as di aposo aches oo. llow fials X-1 ats The higher order term am the top is a f on the bottom is a Divinding & cancelling ast constant Therefore the horizontal asymptote is V=h we get a CS Scanned with CamScanner