p-r-e-c-a-l-c-u-l-u-s

Question

lowkey · Answer

$$f(x)=\frac{ \sqrt{x+4} }{ (x+7)(x-4) }$$
Why would the answer choice be [-4.4)U(4, ∞)

lowkey · Answer

@photonics @Shadow

photonics · Answer

square root of negative numbers aren't defined so on the left hand side it ends at -4.

photonics · Answer

you can't divide by 0 so you have to exclude 4 and -7, but we already excluded -7, so we just take out 4

photonics · Answer

gonna go eat, lmk if you have any questions

lowkey · Answer

$\color{#0cbb34}{\text{Originally Posted by}}$ @photonics
square root of negative numbers aren't defined so on the left hand side it ends at -4.
$\color{#0cbb34}{\text{End of Quote}}$
I'm SO confused.

lowkey · Answer

Why would that fit into the domain

lowkey · Answer

And I know that the domain excludes four because the denominator is x-4 which equals 4, but why isn't seven included
I'm about to cry, I have my precalc final on Friday.

dude · Answer

[-4.4)

|dw:1545267761711:dw|

-4,-3,-2,-1

That is already saying that anything below
<hr class="bbcode_rule" />
Square root functions cannot have a domain less than 0, so the top cannot be less than -4

$\mathbb D$ for $\sqrt{x+4}$: $x\ge -4$

But x cannot be 4 due to the denominator
Hence 
$[-4,4)$ and $(4,∞)$

lowkey · Answer

Why did you do it on a number line...

dude · Answer

To visually show it because [-4,4) already limits anything below (AKA -7)

lowkey · Answer

I'm going to cry what

dude · Answer

You asked why "-7 wasn't included"

It is not expressed because the range of the square root cannot be anything less than -4

lowkey · Answer

What is the role of a numerator on those fraction function thingies

dude · Answer

What

lowkey · Answer

Like what the s h i t does the numerator do, I don't get anythin lmao help

lowkey · Answer

Okay so can I assume that the numerator is the function, then it is changed according to what the denominator says

lowkey · Answer

Wait, nvm, that wouldn't work.

dude · Answer

Usually a numerator is left alone and doesn't affect the vertical asymptotes but since it is a rational function, it does affect

lowkey · Answer

Oh god imma cry I don't understand one point of what that means xD rip.

dude · Answer

Do you know what a vertical asymptote is?

lowkey · Answer

I don't even know what vertical asymptote is, but it's like this|dw:1545269520259:dw|

lowkey · Answer

Where a number is undefined

lowkey · Answer

Where a number is undefined

dude · Answer

Yes

lowkey · Answer

Okay so we know that this one has -7 and 4 as the asymptote. Why does the -7 go away

dude · Answer

Do you know the rule for domains in rational functions? 
$\sqrt{x}$

lowkey · Answer

|dw:1545269707681:dw|
Domain is never negative.

dude · Answer

Yes
$0\le\sqrt{x+4}$
Remove root
$0\le{x+4}$
Subtract 4 on both sides

Domain: $-4 \le x$

This means that the values can only be

-4,-3,-2,-1,0,1...

-7 is already less than this so its dumb to rewrite it for that case because its already excluded

lowkey · Answer

Where did zero and that sign come from

dude · Answer

You said square root functions cannot be negative

so that is where the 0 came from

dude · Answer

It can be 0 or greater

lowkey · Answer

Oh I see, hold on, I'm trying to solve this problem, I'll ask you if it's right

dude · Answer

Okay