Finding domain and range (2 Viewers)

[BlueGas]

I know it's probably a really easy question but how do I find the domain and range?

 

[InteGrand]

I know it's probably a really easy question but how do I find the domain and range?

Depends on the function. Domain means the set of input values for which the function is defined, and range means the set of all possible output values of the function.

 

[DatAtarLyfe]

The easiest way is to graph the function to determine what x-values the function is undefined. Then you can determine the corresponding y-values to determine the range

 

[BlueGas]

If I wasn't to graph the function are there steps for me to follow?

 

[DatAtarLyfe]

Taking the limit as x approaches negative and positive infinite can give you a good idea of the range and then find the domain. There isnt really a specific method to find domain and range as every question has different demands. Its mainly intuition and thinking logically but as a rule you should try find the x-values ie domain first as it's the independent, then use it to find the range

 

[BlueGas]

How about for example the graph: 2x^3 - 3x^2 - 36x + 6, how do I determine the domain and range?

 

[InteGrand]

How about for example the graph: 2x^3 - 3x^2 - 36x + 6, how do I determine the domain and range?

 

[BlueGas]

How would I find the answer to this question?

 

[davidgoes4wce]

 

[BlueGas]

Why did you start the working out with > 0? Why not < 0? Or greater than or equal to?

 

[davidgoes4wce]

Why did you start the working out with > 0? Why not < 0? Or greater than or equal to?

It's a square root sign, so the denominator term has to be greater than 0.

 

[davidgoes4wce]

It also couldn't be greater than or equal to 0, since any number divided by 0, would be undefined.

 

[laters]

There are four main restrictions on the domain. Look for them in this order:
(1) Fractions: the denominator cannot equal 0.
(2) Surds: the inside of the surd must be greater than or equal to 0.
(3) Logs: the inside of the log must be greater than 0.
(4) Inverse trig: for 3 unit kids only.
If you cannot find any of these then your domain is all real values of x.

For the range, if you are given a domain you can test the endpoints as well as any turning points to get an idea (or basically just draw a graph). Sometimes you might use the fact that square roots are positive, or completing the square etc. A more advanced technique reserved for extension 1 kids who have studied inverse functions is you solve for x and apply the above restrictions in a similar way, but to the y-values.

 

[BlueGas]

Just a quick question, I know how to find the domain, I just make the equation > 0 and then whatever x-value I get, I sub that into the range and then that's the range, is this a right method?

 

[keepLooking]

Just a quick question, I know how to find the domain, I just make the equation > 0 and then whatever x-value I get, I sub that into the range and then that's the range, is this a right method?

Yes, that's how you are meant to do it. When you know the domain, you use that to figure out the range.

 

[BlueGas]

Yes, that's how you are meant to do it. When you know the domain, you use that to figure out the range.

So I just sub the x-domain into the function to find the range right?

 

[laters]

So I just sub the x-domain into the function to find the range right?

Like I said before, the the endpoints of the domain are not necessarily the maximum/minimum points. For example there may be max/min points or asymptotes within the domain which are not evident just by looking at the domain so really, you should do a sketch to make sure.

 

[BlueGas]

Okay so here's an example of a question, when they say "for what values is the x function increasing", does that mean what's the domain?

Also what would the domain and range be for this example?

 

[spatula232]

Okay so here's an example of a question, when they say "for what values is the x function increasing", does that mean what's the domain?

Also what would the domain and range be for this example?

Function is increasing where the first derivation is positive, i.e. > 0

That would mean -2 < x < 0 and x > 1 (Assuming your graph is correct)

It can't be Greater than or equal to because at that turning point f'(x)=0 and therefore not >0 (as function is increasing at where f'(x)>0)

 

[BlueGas]

Okay so to find the x values when the function is increasing, I look at the first derivative when it's positive, f'(x) > 0, that's a minimum, so I look at the minimum on the graph?