anonymous
  • anonymous
what is the easy way to find the domain of a function
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Set the denominator to 0 then solve for x
e.mccormick
  • e.mccormick
The main thing is knowing when parts of math are undefined in the number range you are working in. For example, in the real numbers, what are \(\frac{n}{0}\) and \(\sqrt{-n}\).
anonymous
  • anonymous
so how would you find the domain and range of x^2+4x-4

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More answers

e.mccormick
  • e.mccormick
Are there any undefined values in the domain?
anonymous
  • anonymous
i don't think so, we need to find domain
e.mccormick
  • e.mccormick
If there are no undefined values, then it would be.... ?
anonymous
  • anonymous
i guess that is why I'm confused
e.mccormick
  • e.mccormick
Undefined areas are the domain restrictions. No undefined = no restrictions. If there are no restricrtions then....?
e.mccormick
  • e.mccormick
Or another concept for no restrictions is anything is allowed. How would you write that mathematically?
anonymous
  • anonymous
(-infinity, infinity)....?
e.mccormick
  • e.mccormick
\((-\infty,\infty)\) is the domain. So that is that part. Next it the range. And that comes down to what possible answers can you get and is there a highewst or lowest possible answer.
anonymous
  • anonymous
ok so how do you figure that out....just guess? or is there a way to solve for it? where are the infinity signs on the mac?
e.mccormick
  • e.mccormick
\(x^2\), \(x^4\), \(x^6\), and every other even power all basically look like a huge U. Up facing parabola they only have positive values. However, if I said \(x^2-8\) then the low point would be at -8. \(x^3\), \(x^5\), \(x^7\), and so on with odd powers are all some sort of snaking curve with both positive and negative answers.
e.mccormick
  • e.mccormick
I used the \(\LaTeX\) math typograpgy to get my infinity signs. `\((-\infty,\infty)\)` makes \((-\infty,\infty)\). `\(\dfrac{\pi}{2}\)` makes \(\dfrac{\pi}{2}\)
e.mccormick
  • e.mccormick
The equation button lets you do the same thing... but I just type them.
e.mccormick
  • e.mccormick
In calculus, there are ways to find the minimum and maximum. Before calculus, the best ways are to look at a graph or to find the zero points as numbers and see what you have between them.
e.mccormick
  • e.mccormick
So look at this graph and see what range values (y values) are possible: https://www.desmos.com/calculator/zrxb999hsa
anonymous
  • anonymous
so how would you do the sqrt of 3x-4+2
e.mccormick
  • e.mccormick
\(\sqrt{3x-4+2}\) `\(\sqrt{3x-4+2}\)` Well, where is it that the stuff under the root is \(\ge 0\)?
anonymous
  • anonymous
i dont know im confused
e.mccormick
  • e.mccormick
And is it really written that way? Because that is the same as: (\sqrt{3x-2}\)
anonymous
  • anonymous
the 2 isnt under the sqrt
e.mccormick
  • e.mccormick
Or was the +2 supposed to be outsuide or something? Kk. \(\sqrt{3x-4}+2\)
anonymous
  • anonymous
yea like that!
e.mccormick
  • e.mccormick
So, they key here is what is under the root. \(3x-4\ge 0\)
e.mccormick
  • e.mccormick
Now, solve that for x.
anonymous
  • anonymous
x is greater than or equal to 4/3?
e.mccormick
  • e.mccormick
Yes. That is the valid domain. As for the range, well, you now know the smallest value of x. Put it in! Solve for that, and the answer is the starting point of the range. Then you try another value of x, a larger one, and see if things go up or down from the starting point. That gives you the range.
anonymous
  • anonymous
but my teacher has us do the domain and range as a set of points so would the domain be (4/3, infinity)?
e.mccormick
  • e.mccormick
Yep. And it is not a set of points. It is more like set notation.
anonymous
  • anonymous
thats what i meant sorry, thanks for all the help!
e.mccormick
  • e.mccormick
And it is still worth it to graph it. That graphing utility I linked for the other one will also do roots.
anonymous
  • anonymous
ok thanks!
e.mccormick
  • e.mccormick
The big deal about graphing some of these after the fact is that it is a great way to check your answers. Also, it helps you match up between the number results and the visual results. Since visual memory is 70% of sensory memory, the other 30% being the other 4 senses, it is a very powerful way to remember things.
anonymous
  • anonymous
ok ill make sure to graph them also! thanks!
e.mccormick
  • e.mccormick
And as long as you remember that x=domain and y=range, that is all you need for the checking the answers part for these type questions.
e.mccormick
  • e.mccormick
Checking with a graph, that is.

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