Question

Which graph represents the function of f(x) = the quantity of 9 x squared plus 9 x minus 18, 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 3, with discontinuity at negative 2, negative 9
graph of 3 x minus 3, with discontinuity at 2, 3

Answer 1

One moment, let me see.. :)

Answer 2

Show YOUR work, first. Let's see what YOU get - sure or not.

Answer 3

Yes please do.

Answer 4

i have no work on this one, i dont know how to even start! lol

Answer 5

Okay well is this what you mean?

\[f(x) = \frac{ 9x^2 + 9x - 18 }{ 3x + 6 }\]

Answer 6

Insufficient response.

Some notational improvement would also be helpful.

f(x) = the quantity of 9 x squared plus 9 x minus 18, all over 3 x plus 6?

This is a good representation.
f(x) = (9x^2 + 9x - 18)/(3x+6)

With a little LaTex, you can write it as Aihber has suggested.

Please demonstrate that you can factor the Denominator.

Answer 7

Well to start you off, so you can at least START... try factoring on your own. :)

Can you do that?

@princesssleelee

Answer 8

i do not know how

Answer 9

Okay well lets start with \(3x\) and \(6\)

Answer 10

What is a common factor between those two?

Answer 11

3

Answer 12

Right! So can you try and rewrite \(3x + 6\) while pulling out a 3?

Answer 13

Hmm... I know the way I said it was a bit confusing.

So let me explain further.

Answer 14

You MUST be able to factor the Denominator. You CANNOT solve this problem without these basic skills. If you have been given this problem without ANY exposure to such factoring, then whoever gave you the problem is an incompetent clod. Hoping to believe that your teacher is more capable than that, I choose to believe that you CAN factor the denominator.

Answer 15

3x-3 is the entire function factored, correct?

Answer 16

I appreciate you trying! :)

Unfortunately, that is incorrect. Also, it is better if you are able to use parenthesis.

Also, why did you get a minus sign instead of a plus sign?

Can you try again?

Answer 17

then i have no idea how to do it

Answer 18

That's the spirit. Look really hard at the function of the Distributive Property:

a(b+c) = ab + ac

It goes the other way, too.

de + df = d(e+f)

Do that with (3x+6). Find a factor that is common when comparing '3x' and '6'.

Answer 19

this is just so confusing

Answer 20

Yes, I know. It is a bit confusing. Well, I am not sure why you changed \(3x + 6\) into a subtraction problem. It should stay positive. So other than that you are correct. Instead of \(3x-2\) it would be \(3(x + 2)\)

Answer 21

Do you see that? :)

Answer 22

Note: If you cannot factor the denominator, you have no prayer of factoring the numerator, which is your next task.

Just look at the rule and apply it. It doesn't have to be confusing. Waiting for it to bite you is a little confusing. Logically address the rule. Logically address the given problem statement.

Answer 23

Right :)

Answer 24

But, do you see how I did that?

@princesssleelee

Answer 25

Take your time to evaluate.

Answer 26

yes i do for the most part.

Answer 27

then distribute?

Answer 28

No you would not distribute. If you did, you would get the same thing as before. Factoring is basically undoing the fact that you distributed.

So, now we do the same with the numerator.

Do you think you can factor \(9x^2 + 9x -18\)?

Answer 29

well they all go into 9

Answer 30

x2+x-2

Answer 31

Right!!

\[x^2 + x - 2\]

Answer 32

Now, what are two integer numbers that multiply to be \(-2\) and add up to be \(1\)?

Answer 33

Because, we must continue factoring.

Answer 34

1 and -2

Answer 35

nevermind thats wrong

Answer 36

You have the numbers right but the positive and negative signs mixed up. Can you try again?

Answer 37

Yes, try again :)

Answer 38

2 and -1

Answer 39

Right! So the factors would be:

\((x + 2)\) and \((x - 1)\)

Answer 40

Do you see that?

Answer 41

yes

Answer 42

Okay so, \(9x^2+9x-18\) is now \(9(x+2)(x-1)\)

Answer 43

So it would completely be:

\[f(x) = \frac{ 9(x + 2)(x - 1) }{ 3(x + 2) }\]

Answer 44

Do you see that?

Answer 45

yes

Answer 46

We can't divide by 0 meaning that \(x+2\) can't be 0.

However, \(x+2\) can be 0 when \(x\) is... what?

Do you know?

@princesssleelee

Answer 47

-2

Answer 48

Right so

\[f(x) = \frac{ 9(x + 2)(x - 1) }{ 3(x + 2) } = 3(x - 1), x \neq -2\]

Answer 49

Do you see that?

Answer 50

This just means that our function will not exist at \(x = -2\)

Answer 51

ok

Answer 52

So... if we have \(f(x)=3x-3\), then the y-intercept is -3. Right?

We also know that \(f(-2)=3(-2)-3=-6-3=-9\)

Now when graphing... we would draw a line going through \((0,-3)\) and \((-2,-9)\)

However, we will erase the one point at (-2,-9) since our function shouldn't exist there

Answer 53

So the graph should look something like this: