I do not understand how I missed this question. I used parentheses at the beginning instead of brackets and the instructor is not helping me in any way to figure it out. Can someone explain it to me?

Question

I do not understand how I missed this question.  I used parentheses at the beginning instead of brackets and the instructor is not helping me in any way to figure it out.  Can someone explain it to me?

anonymous · Answer

attachment

psymon · Answer

*looks*

anonymous · Answer

I submitted a word document with the equation.  I think it's still working on the upload

psymon · Answer

Well, parenthesis means you do not include the number -3. But if you plug in -3 into your function for x, you get a legit answer, meaning it's a bracket. It's only a parenthesis if that value makes the function undefined or if its with infinity signs.

anonymous · Answer

I don't understand.  I'm not real good at math and all the other ones like this one that I put parenthesis I got correct.  This one I got wrong.  That's why I'm so confused

psymon · Answer

Well, do you understand the difference between using parenthesis or using a bracket, or is that what we don't get?

psymon · Answer

Ah, okay. Well, the difference is basically the same as whether or not you use
$$< or \le $$. The first one means do not include the number and the 2nd one does mean include it. It's the same thing with parenthesis and brackets. A parenthesis means we do not include the number and a bracket means we do include the number. I'll show ya the difference with actual functions.

psymon · Answer

$$2\sqrt{x+3}+2$$
This graph goes from -3 to infinity. The question is does -3 actually exist or is that a starting point? Well, if I replace x with -3.....
$$2\sqrt{-3+3}+2 = 2\sqrt{0}+2 = 2$$ Nowhere did I get an undefined answer. Since I did not come up with something impossible, I can include -3 and therefore would put a bracket. Here is something where that is not true:

$$\frac{ 2 }{ \sqrt{x+3} }+2$$Same thing with this graph, we go from -3 off to infinity. But if I plug in -3 for x....

$$\frac{ 2 }{ \sqrt{0} }+2 = UNDEFINED$$ We can't have a 0 in the denominator. SInce -3 made my function undefined, I have to put a parenthesis with -3 instead of a bracket. 

So what's the difference? Brackets mean the value of x does exist and does not make the answer undefined. Parenthesis means we start or end at that point, but we cannot include that point because it makes the function undefined. Kinda make some sense?

anonymous · Answer

OK!  Thank you!  Now I get it.  to a point. But I still understand better than what I did.   Thank you VERY VERY MUCH!

psymon · Answer

Yeah, np ^_^ One last note. Infinity and negative infinity ALWAYS have parenthesis, never will you use brackets with infinity signs.

anonymous · Answer

Thank you! That helps alot.

psymon · Answer

Glad it helps. Good luck ^_^