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Consider the function: f(x)= x ____ x+1 (a) Determine the domain of f(x). (b) Fi

ID: 3287725 • Letter: C

Question

Consider the function: f(x)= x ____ x+1 (a) Determine the domain of f(x). (b) Find the x-intercept(s) (if any). (c) Find the y-intercept(s) (if any). (d) Determine the behavior of f(x) for large absolute value of x (e) Find all horizontal and vertical asymptotes of f(x). (f) Find the interval(s) where the function is increasing and the inter- val(s) where it is decreasing. (g) Find all relative maxima and relative minima (if any) 4(h) Find the interval(s) where the function is concave up and the inter- val(s) where the function is concave down. (i) Find all in ection point(s) (if any). (j) Sketch the graph of f(x).

Explanation / Answer

f(x) = x/(x+1) ;

a) Domain is R except x = -1 ;

Domain = ( -infinity ,-1) union (-1,infinity) l

c) y = 0

at x = 0 ---x-intercept ;


b) x =0 ...y =0 ---y-intercept


d) as x tends to infinity f(x) tends to 1 ;

e) x =-1 ;