Question

what is the easy way to find the domain of a function

Answer 1

Set the denominator to 0 then solve for x

Answer 2

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 \(\sqrt{-n}\).

Answer 3

so how would you find the domain and range of x^2+4x-4

Answer 4

Are there any undefined values in the domain?

Answer 5

i don't think so, we need to find domain

Answer 6

If there are no undefined values, then it would be.... ?

Answer 7

i guess that is why I'm confused

Answer 8

Undefined areas are the domain restrictions. No undefined = no restrictions. If there are no restricrtions then....?

Answer 9

Or another concept for no restrictions is anything is allowed. How would you write that mathematically?

Answer 10

(-infinity, infinity)....?

Answer 11

\((-\infty,\infty)\) 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.

Answer 12

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?

Answer 13

\(x^2\), \(x^4\), \(x^6\), 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.

Answer 14

I used the \(\LaTeX\) math typograpgy to get my infinity signs. `\((-\infty,\infty)\)` makes \((-\infty,\infty)\).

`\(\dfrac{\pi}{2}\)` makes \(\dfrac{\pi}{2}\)

Answer 15

The equation button lets you do the same thing... but I just type them.

Answer 16

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.

Answer 17

So look at this graph and see what range values (y values) are possible:
https://www.desmos.com/calculator/zrxb999hsa

Answer 18

so how would you do the sqrt of 3x-4+2

Answer 19

\(\sqrt{3x-4+2}\) `\(\sqrt{3x-4+2}\)`

Well, where is it that the stuff under the root is \(\ge 0\)?

Answer 20

i dont know im confused

Answer 21

And is it really written that way? Because that is the same as:
(\sqrt{3x-2}\)

Answer 22

the 2 isnt under the sqrt

Answer 23

Or was the +2 supposed to be outsuide or something?

Kk.

\(\sqrt{3x-4}+2\)

Answer 24

yea like that!

Answer 25

So, they key here is what is under the root.

\(3x-4\ge 0\)

Answer 26

Now, solve that for x.

Answer 27

x is greater than or equal to 4/3?

Answer 28

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.

Answer 29

but my teacher has us do the domain and range as a set of points so would the domain be (4/3, infinity)?

Answer 30

Yep. And it is not a set of points. It is more like set notation.

Answer 31

thats what i meant sorry, thanks for all the help!

Answer 32

And it is still worth it to graph it. That graphing utility I linked for the other one will also do roots.

Answer 33

ok thanks!

Answer 34

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.

Answer 35

ok ill make sure to graph them also! thanks!

Answer 36

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.

Answer 37

Checking with a graph, that is.