How do I find the domain of this function?

- anonymous

How do I find the domain of this function?

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- anonymous

\[g(x) \sqrt{x^2 - 3x - 40}\]

- anonymous

I have \[\sqrt{(x-8)(x+5)} \]

- anonymous

\[(x-8)(x+5) \ge 0\]

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## More answers

- anonymous

The original problem is at the top.

- anonymous

Draw a number line and see for it

- anonymous

I don't know what x can't be though

- anonymous

I know the answer but I don't know how to get the answer.

- anonymous

(-infinity , 5] U [8 , infinity)

- anonymous

yeah but how do I find that?

- anonymous

just do trial and error method...)

- anonymous

(x−8)(x+5)≥0

- anonymous

luk for the vlue of x which satisfies this...

- anonymous

There must be a logical way to find the answer, right?

- ganeshie8

(x-8)(x+5) >= 0
its a parabola, right ?

- anonymous

I could input it into my graphing calculator but other wise I don't know how to tell if its a parabola or not.

- ganeshie8

y = ax^2 + bx + c is a parabola

- ganeshie8

any quadratic function gives a parabola graph

- anonymous

ok

- ganeshie8

can you find the x intercepts ?

- ganeshie8

once you find x-intercepts, you would know where the parabola dips into x axis (goes negative)

- ganeshie8

|dw:1346519548989:dw|

- anonymous

Oh ya that would be the point at which the g(x) function is 0, so its x - 8 = 0, x = 8, x+ 5 = 0, x=-5, and since its a parabola the graph only passes through zero twice. Nice dude, so the domain is (-infinity, -5] U [8, +infinity]

- ganeshie8

yeah nice you got it :)

- anonymous

@ganeshie8

- anonymous

Awesome, thanks again. Is there a way I could recognize any graph's shape or at least some and would you recommend memorizing those?

- ganeshie8

if the degree is 2, then its a parabola

- ganeshie8

finding domains for other polynomials is bit tricky... as they may dip into x-axis multiple times

- anonymous

okay

- ganeshie8

do you knw sketching polynomilas (end behiavior thingy )

- anonymous

never heard of it

- ganeshie8

end behavior helps you sketch ANY polynomial freehand

- anonymous

Thanks dude, I'll look it up

- ganeshie8

process is basically :
1) find x intercepts
2) using end-behavior sketch the graph by hand

- ganeshie8

its easy concept and worth learning... im sure you wil get hang of it in few minutes....... good luck :)

- anonymous

why is it that a polynomial with a degree of two is a parabola?

- anonymous

Thanks again.

- ganeshie8

uhh il have to think...... idk exactly... i think it has something to do with local maximum/minimum + increasing/decreasing thingy. we need to turn to calculus for proper understanding. im also learning... . so im no good for answering this :(

- ganeshie8

@mukushla @eliassaab @experimentX

- anonymous

Oh, I have enough to learn for now so it doesn't matter to me. I bet I wouldn't understand the explanation if it involves terms I've never had before haha.

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