+0  
 
0
97
2
avatar+56 

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...

UpTheChels  Sep 15, 2017
Sort: 

2+0 Answers

 #1
avatar+78719 
0

 

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

 

 

cool cool cool

CPhill  Sep 15, 2017
 #2
avatar+56 
0

God d**n, I hate reciprocals. Thanks so much CPhill, your help is appreciated. 

UpTheChels  Sep 15, 2017

6 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details