Find the range of the function

\(f(x) = \frac{x^2 + 14x + 9}{x^2 + 2x + 3},\)

as x varies over all real numbers.

SpicyP Apr 23, 2020

#1**+1 **

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

Guest Apr 23, 2020

#1**+1 **

Best Answer

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

Guest Apr 23, 2020

#2**0 **

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?

Melody Apr 23, 2020

#3

#4**0 **

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. :///

Melody
Apr 23, 2020