+133 Find the range of the function
\(f(x) = \frac{x^2 + 14x + 9}{x^2 + 2x + 3},\)
as x varies over all real numbers.
lmao since no one is on atm and u need help asap heres calculator doing it for you
https://www.symbolab.com/solver/step-by-step/range%20%5Cfrac%7Bx%5E%7B2%7D%2B14x%2B9%7D%7Bx%5E%7B2%7D%2B2x%2B3%7D
lmao since no one is on atm and u need help asap heres calculator doing it for you
https://www.symbolab.com/solver/step-by-step/range%20%5Cfrac%7Bx%5E%7B2%7D%2B14x%2B9%7D%7Bx%5E%7B2%7D%2B2x%2B3%7D
+118608 Thanks guest, that SYMBOLAB calculator site is super cool.
It gets the answer with working!
I've never done this type of question before and to be honest, although I can follow their algebra, I do not have a full understanding of what it is doing.
How do I interpret the relevance of discriminant of expressions like that one.
I also found the axis of symmetry of that expression and it gave me the equation of a hyperbola which does give the graph symmetry.
Super weird, super cool!
Can anyone off me more insight into the logic of this question, and the answer given by that calculator?
+118608 Thanks very much.
The video did not really explain more but while I was watching it I had a light bulb moment.
I suddenly had insight into why it would work.
So yes, the video was both interesting and very helpful. Thank you HELPMEEEEE 
Now I just hope I can remember it for next time. :///
