Please help me. Given the function: f(x) = (x+2)/(x^2+1), what is its range? How would I find it?

PS: DON'T YOU HATE IT WHEN YOU POST YOUR QUESTION, AND PEOPLE KEEP ON PILING THEIR QUESTIONS ON TOP OF YOURS, AND YOUR QUESTION GETS LOST IN THE MIX??? I HATE THAT!!!

Question

Please help me. Given the function: f(x) = (x+2)/(x^2+1), what is its range? How would I find it?


PS: DON'T YOU HATE IT WHEN YOU POST YOUR QUESTION, AND PEOPLE KEEP ON PILING THEIR QUESTIONS ON TOP OF YOURS, AND YOUR QUESTION GETS LOST IN THE MIX??? I HATE THAT!!!

anonymous · Answer

im watching you

anonymous · Answer

I'm not really sure how to get the exact range with the tools I have. With calculus we would take the 1st derivative (think a function that gives you the slope at any point along the curve), set it = 0, and the values of x where it equals 0 would be our points of maximum and minimum (you'd still have to evaluate the function there to get the actual maximum and minimum). I'm attaching a graph of the area of interest, with vertical lines marking the spot where the maximum and minimum values occur. I'm sorry but I'm going to have to leave as I'm being picked up momentarily to go out for the evening.

anonymous · Answer

Ariyana what are you talking about?

anonymous · Answer

http://www.wolframalpha.com/input/?i=(x%2B2)%2F(x%5E2%2B1)

anonymous · Answer

:)

anonymous · Answer

You will almost never use calculus to find the range because it's extremely tedious. It's best to turn to technology