Question

Which statement about the graph of the rational expression (x^2+6x+9)/(x^2-4) is true?

The function is above the x-axis between -2 and 2
The function is above the x-axis for x>2
The function is below the x-axis for x<-2
The function is below the x-axis between -3 and -2

Answer 1

@tcarroll010 can you help me on my last 5 questions of my review please

Answer 2

wait is it c

Answer 3

The first thing you would want to do is find the vertical asymptotes. This will help you identify intervals.

No, the answer is not "c".

Answer 4

wait nvm

Answer 5

the VA are x=-2 and x=2 but does that mean the answer is a?

Answer 6

You can graph the function, or you can actually solve this one by factoring the numerator and denominator and you'll be able to see how the factors will be either pos/neg for certain domains.

No, it's not "a" either.

Answer 7

\[\frac{ (x + 3)^{2} }{ (x + 2)(x - 2) }\]

Answer 8

Hint:

If x > 2, then what sign are all the factors?

Answer 9

positive

Answer 10

So, if all factors are positive, then the whole expression is positive and the values lie above the x-axis for x > 2.

Answer 11

Visual confirmation:

Answer 12

See that, @venom936 ? I'm sure you do, because you are catching on well. I grpahed it for a little reinforcement for you.

Answer 13

how do you input the equation into the calculator bc every time i do i get a different graph than yours

Answer 14

It's been many years since I used your brand calculator. so I have to refer you to meta-calculator online. It's easy to use. I use the old version because there are some bugs in the new version. For the old version, you have to use "*" symbol for multiplication. Website:
http://www.meta-calculator.com/online/

Answer 15

alright thanks for the tip

Answer 16

Take a look: