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# Properties of this reciprocal function? f(x) = (x+1)/(x-1)

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the function is  f(x)= (x+1)/(x-1). i need to find the following properties-

domain, range, any restrictions, intervals of increasing and decreasing, the x and y-intercepts, and vertices.

so far i have, domain - (xER|x≠1)
range - im not sure
restriction x≠1 (are there any other restrictions?)
interval of increase - none
interval of decrease - im not sure
roots x=-1
Y INT  y=-1
Vertice- im not sure

can someone please help me out? im not sure how correct i am to begin with. correct me please if im wrong. ive always hated reciprocal functions...

Sep 15, 2017

#1
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f(x)  =  [ x + 1 ] / [ x - 1]

Look at the graph :

Domain .....all values except any x that makes the denominator  = 0....thus, x = 1 isn't in the domain

Range  .....we  have the same power polynomials in the numerator as in the denominator.....thus, we will have a horizontal asymptote  given by the ratio of  the coefficient on the highest power of x's in both numerator and denominator.....the highest powers  of x have the ratio of coefficients =   1 / 1   = 1  ......thus....we will have a horizontal asymptote at  y  = 1

So   the range   is  ( -infinity , 1 ) U ( 1 , infinity)

Restrictions  - you are correct

Interval of increase   -you are correct

Intervals of decrease......  the function decreases from (-infinity, 1)  and from (1, infinity)

Roots..... - you are correct

Y intercept - you are correct

Vertices  - since we have no minimums or maximums on this graph......there are no vertexes

Sep 15, 2017
#2
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God d**n, I hate reciprocals. Thanks so much CPhill, your help is appreciated.

UpTheChels  Sep 15, 2017