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 ;