Question

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

Answer 1

@whpalmer4

Answer 2

@Luigi0210

Answer 3

@lalaly

Answer 4

@beccaboo333
please help

Answer 5

@alias

Answer 6

@AccessDenied

Answer 7

Do you know how to factor a difference of squares? If you notice, your numerator is a difference of squares, and in the denominator looks like one of those factors.

Answer 8

I'm just confused still I'm sorry

Answer 9

@Destinymasha

Answer 10

Factoring, we would take: \(a^2 - b^2 = (a + b)(a - b)\)
So now look at the numerator of the fraction.

\( 9x^2 - 36 \)
9 = 3^2, and 3^2 x^2 = (3x)^2. 36 = 6^2.
So we do have a difference of squares, right?
(3x)^2 - 6^2

Answer 11

right

Answer 12

But then what do you do

Answer 13

So to factor, let's compare the two. I highlight that a=(3x) and b=6:
\( \color{blue}{a}^2 - \color{green}{b}^2 = (\color{blue}{a} + \color{green}{b})(\color{blue}{a} - \color{green}{b}) \)
\( \color{blue}{(3x)}^2 - \color{green}{6}^2 = (\color{blue}{(3x)} + \color{green}{6})(\color{blue}{(3x)} - \color{green}{6}) \)
Now if we rewrite our numerator as (3x + 6)(3x - 6), notice that the denominator also has a factor of 3x + 6. You can cancel those out, right? (As long as x is not -2).

Answer 14

sorry my computer froze, and yes.

Answer 15

I think it was OpenStudy that time.
But, yes, so if we substitute that part in:
\( \displaystyle f(x) = \dfrac{(\color{reD}{3x + 6})(3x - 6)}{\color{red}{3x + 6}} \)
We can cancel these two factors for most cases.
BUT, 3x + 6 cannot equal 0. Otherwise, we have 0/0 which is not well defined!
3x + 6 = 0 when x= -2 (Solving for x). So we will have no point at x= -2.
And then we cancel the factors to be 1.
\( \displaystyle f(x) = 3x - 6 \qquad x \ne -2 \)
Can you find the graph of this equation among those listed?

Sorry to rush a bit, I have to go soon!

Answer 16

wait so would it be -2

Answer 17

I've been doing math all day I'm sorry my brain is fried. is that not it?

Answer 18

What were you asking would be -2? That is the point where the graph is undefined. Because 3*(-2) + 6 = -6 + 6 = 0, and in our original equation we get a division by zero error. So we exclude it there.

Answer 19

I don't see which graph I would choose from that?

Answer 20

You know which graph has the equation y = 3x - 6?
I think both C and D have that graph. But one graph has an open circle where x= -2, and one where x = 2.
You want the one where the open circle is on -2.

Sorry, I have to leave now! If you still need help, please bump the question or tag others! Hoping I have left enough information to make it clear.

Answer 21

ohh! thank you!!

Answer 22

Glad to help! and bye!

Answer 23

bye :)