Range of Rational Functions...1

[nycmathguy]

I have a hard time finding the range of functions, especially rational functions.

For f(x) = 1/(x + 1), find the range algebraically. Also, graph the function and find the range by looking at the graph of f.

Note: I understand the range to be the y-value of the point (x, y). Yes?

 

[MathLover1]

f(x) = 1/(x + 1)
graph it

as you can see from the graph, range is: f(x)<0 or f(x)>0

Range of : 1/(x+1)
the set of values of the dependent variable for which a function is defined

since f(x)=0 if x=-1 ,a function will be undefined
a function is defined f(x) not = to 0

so, range is:
f(x)<0 or f(x)>0

Interval notation:
(-infinity ,0) U (0, infinity )

 

[nycmathguy]

f(x) = 1/(x + 1)
graph it


View attachment 490

as you can see from the graph, range is: f(x)<0 or f(x)>0

Range of : 1/(x+1)
the set of values of the dependent variable for which a function is defined

since f(x)=0 if x=-1 ,a function will be undefined
a function is defined f(x) not = to 0

so, range is:
f(x)<0 or f(x)>0

Interval notation:
(-infinity ,0) U (0, infinity )

Is there an algebraic way to find the range?