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

#1**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

CPhill
Sep 15, 2017

#2**0 **

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

UpTheChels
Sep 15, 2017