SOLUTION: find the range and domain. f(x)=1/x+2

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Question 113011: find the range and domain.
f(x)=1/x+2
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=%281%29%2F%28x%2B2%29 Start with the given function


x%2B2=0 Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of x that make the denominator zero, then we must exclude them from the domain.



x=0-2Subtract 2 from both sides


x=-2 Combine like terms on the right side





Since x=-2 makes the denominator equal to zero, this means we must exclude x=-2 from our domain

So our domain is:

which in plain English reads: x is the set of all real numbers except x%3C%3E-2

So our domain looks like this in interval notation



Now to find the range, notice that there isn't an x term in the numerator. So if
%281%29%2F%28x%2B2%29=0, there isn't an x value that will satisfy the equation. So in other words, f%28x%29=%281%29%2F%28x%2B2%29 will never be equal to zero. So this means we must take 0 out of our range.



So our range is:

which in plain English reads: y is the set of all real numbers except y%3C%3E0

So our range looks like this in interval notation



Now let's graph f%28x%29=%281%29%2F%28x%2B2%29

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%281%29%2F%28x%2B2%29%29+


So we can see that at x=-2 there is a gap (the vertical piece is not part of the graph) and at y=0 there is an asymptote. So this verifies our answer.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=1%2Fx%2B2
the domain is all real numbers R except x=0; you can't divide by zero and get a real number
the domain D is:(-infinity,0) U :(0,infinity )
and range is: R-0