Question

Which graph represents the function of f(x) = the quantity of 9 x squared minus 36, all over 3 x plus 6?

graph of 3 x plus 6, with discontinuity at 2, 12
graph of 3 x plus 6, with discontinuity at negative 2, 0
graph of 3 x minus 6, with discontinuity at negative 2, negative 12
graph of 3 x minus 6, with discontinuity at 2, 0

Answer 1

Okay.

Can you show me your work or at least try to solve? It is exactly like the previous question that I helped you with, which took a lot of explaining :)

@princesssleelee

Answer 2

well first find the common factor in the denominator.

Answer 3

which is 3.

x+2

Answer 4

correct?

Answer 5

Right... \(3(x + 2)\)

Answer 6

So we are simply factoring again.

We would take \(a^2−b^2=(a+b)(a−b)\)

Now lets look at the numerator, shall we?

\(9x^2−36\)

We know that \(9 = 3^2\) and that \(3^2 x^2 = (3x)^2\)

Then, \(36 = 6^2\)

Now, when looking at this we do have a difference of squares, correct?

Which is... \((3x)^2 - 6^2\)

Answer 7

yes

Answer 8

So now lets just factor and substitute in our numbers.

\( a^2−b^2=(a+b)(a−b)\)

We know that \(a = (3x)\) and \(b = 6\)

Right?

Answer 9

right

Answer 10

Okay, now lets just substitute in our values.

\((3x)^2−6^2=((3x)+6)((3x)−6)\)

Now let's "explore" and "experiment" a bit. If we were to rewrite the numerator and change it to \((3x + 6)(3x - 6)\) and look at the fact that the denomination has a factor of \(3x + 6\), we can cancel those out... right?

Answer 11

right

Answer 12

because the signs are opposite meaning they cancel.

Answer 13

Good Job! Now let's complete the "experiment" shall we?

So if we were to substitute that part in, it would look like this:

\(f(x)=(3x+6)(3x−6)3x+6\)

We can simply cancel these two factors out.

However, \(3x + 6\) can't equal 0.

We know that \(3x + 6 = 0\) when \(x = -2\). This means that we will not have any point at \(x = -2\)

Now we can cancel the factors to equal 1.

\(f(x)=3x−6x≠−2\)

Now can you try finding the graph of those answer choices?

Answer 14

i know it is not A

Answer 15

Okay. Continue...

Answer 16

its below -2 so C and D are my options, right?

Answer 17

Right! Now what...

Answer 18

well, i have to determine the plotted point

Answer 19

You see...

You want the one where the point is on -2.

Can you figure it out now?

Answer 20

leading to graph C! its x-axis is on -2

Answer 21

Awesome!

Answer 22

Hope this helped! Have a great day! :)

A medal would also be appreciated! Just click best response next to my name!

Also, a fan would be appreciated as well! Just hover over my icon and click "Become A Fan". This will allow you to see every time I am online! :)

If you see that I am online and need help with a question, just tag me in your question!

@princesssleelee

Answer 23

Already a fan! and i truly appreciate it !!!

Answer 24

No problem! If we are finished... please close this post :)

Answer 25

the last one we did was not letter D....

Answer 26

Great. Why don't you prove what it WAS and how you managed the appropriate response.

Answer 27

This one?

Answer 28

Yes

Answer 29

We didn't choose letter D for this one..

Answer 30

oh goodnesss.. thats the one i selected :(

Answer 31

Aw... we chose C! :(

Answer 32

OH NO the one before

Answer 33

the last post

Answer 34

c was correct :)

Answer 35

Awesome!

Answer 36

its okay, im not going to retake it.. that took way too long!

Answer 37

an 80% will jut have to do, even though the rest are all 100%'s lol ;)