Question

Can anyone lend a hand at finding the range of a function? :)

So.. I have this problem. f(x) = 1/x-7 + 2
I've tried to get this on my own, but I just can't. I feel silly. Especially since it seems like such an easy concept! I know how to find the domain alright, but the range just puzzles me. This is a question from a practice test, and I have the answers, but I can't find my way to get it... The answer is that:
Domain: All real numbers except 7
Range: All real numbers except 2

So, would anyone mind lending a hand? Any help is appreciated. I'd just really like to pin down how to find the range once and for all. :)

Answer 1

\(\color{#000000 }{ \displaystyle f(x)=\frac{1}{x-7}+2 }\)

Answer 2

Domain of the function := all x-values that you are capable of plugging into the function

Range of the function := all y-values that can possible get (as an output) from the function

Answer 3

Range will depend on the domain.

Answer 4

You probably know that

\(\color{#000000 }{ \displaystyle \frac{ 1 }{x-7} \ne0 }\)

Because there isn't an x-value that would satisfy this equation.
And therefore,

\(\color{#000000 }{ \displaystyle \frac{ 1 }{x-7}+2 \ne2 }\)

So, you can see that f(x) is never equal to what number?
(Note, that you can possible get absolute any output, besides that one number that you may never get,)

Answer 5

You sir, are magic.
I think I finally get it.

Thank you so much for the help, seriously! :D

Answer 6

You are welcome!