Question

I need to find the excluded value:
y = 3 / x + 4

Answer 1

\[y = \frac{3}{x+4}\]or\[y = \frac{3}{x} + 4\]?
In either case, find the value of \(x\) that causes a division by 0.

Answer 2

Hm..
3 x 4
\[12 \div x\]
I'm guessing that's what it is?

Answer 3

Which of the two problems that I listed is the correct one?

Answer 4

the second?

Answer 5

Is it or isn't it? I can't see your assignment, so you need to tell me :-)

Answer 6

I think so. It isn't multiple choice, unfortunately.

Answer 7

No, multiple choice has nothing to do with this — which of my equations matches what is printed on your page? The two are NOT equivalent.

Answer 8

Oh, I see what you are saying. I thought it was
\[\frac{ 3 }{ x } + 4\]
It is in fact, the first one.

Answer 9

Let's assume that it is the second one.
\[y = \frac{3}{x} + 4\]Is there a value of \(x\) that causes you to divide by 0 when you use that equation?

Answer 10

No. You can't divide by zero.

Answer 11

What happens if you try to find the value of \(y\) when \(x = 0\)?

Answer 12

Sigh, now I see you responded as I did, and I'm doing the other problem. Well, let's finish this one, and then do the other, you'll get two for the price of one :-)

Answer 13

Ok, so that would be dividing by 0 as well?

Answer 14

Yes, so x=0 would be an excluded value for the equation \[y = \frac{3}{x}+4\]

Now let's find the excluded value for \[y = \frac{3}{x+4}\]What value of \(x\) would cause us to attempt to divide by 0 there?

Answer 15

Put differently, \[x+4 = 0\]\[x = ?\]

Answer 16

\[x = -4\]

Answer 17

Right! At x=-4, there is no defined value for y in that equation, so x=-4 is the excluded value.

Answer 18

Here are graphs of both equations that show what happens:

The blue line represents \[y=\frac{3}{x}+4\] and the purple line represents \[y=\frac{3}{x+4}\]

Answer 19

Ok, thanks!

Answer 20

I see that there is one purple straight line. Does that represent \[y = \frac{ 3 }{ x + 4 }\]
as well?

Answer 21

Well, that's an artifact, it shouldn't really be there because there is no single value of y at that x-value. There's a similar blue line, you just don't easily see it because it coincides with the x-axis at x = 0.

Answer 22

Think about what happens as you move along the x-axis from x = 1 to very close to x = 0 (but still x > 0) — the value of y gets really, really large. Then if you jump over to the other side, the value is just as large, but opposite in sign. The graphing program didn't lift the pencil off the paper as it went from +infinity to -infinity, so we got that spurious vertical line :-)