domain and range (1 Viewer)

[jjuunnee]

How do I find the domain and range of functions without having to draw it out or know the graph?

I know for functions that have a square root the value under the square root can't be negative, or in a fraction the denominator cannot be zero, etc, so figuring out the domain isn't too hard, but what about range? Is there some algebraic method I can use to find the range or, as mentioned before, do I need to know the graph?

 

[Green Yoda]

domain is where x values are permissible..so find out the limits of where x is not defined and find the domain from there. E.g. y=1/x d:all real x, x=/=0 as it will be not defined.

Range is where y values are permissible..for example |x|, for this the y out comes will always be positive so r: y>=0.

 

[eyeseeyou]

We have 4 rules for Domain:

1.Fraction. Bottom cannot equal to zero
2. Surds. Squareroot of bracketed equation, bracketed equaion is greater than or equal to zero
3.Logs. log (bracketed equation). Bracketed equation is greater than 0
4. Inverse trig. In later years

What would the rules be for the range?

 

[eyeseeyou]

We have 4 rules for Domain:

1.Fraction. Bottom cannot equal to zero
2. Surds. Squareroot of bracketed equation, bracketed equaion is greater than or equal to zero
3.Logs. log (bracketed equation). Bracketed equation is greater than 0
4. Inverse trig. Later

What would the rules be for the range?

 

[InteGrand]

We have 4 rules for Domain:

1.Fraction. Bottom cannot equal to zero
2. Surds. Squareroot of bracketed equation, bracketed equaion is greater than or equal to zero
3.Logs. log (bracketed equation). Bracketed equation is greater than 0
4. Inverse trig. Later

What would the rules be for the range?

Inspection.

 

[eyeseeyou]

Inspection.

???Im pree sure there are rules for range given that there are rules for domain

Anyways give me an example of "Inspetion"? It's so consuing when you said that integrand

 

[Green Yoda]

???Im pree sure there are rules for range given that there are rules for domain

Anyways give me an example of "Inspetion"? It's so consuing when you said that integrand

As I have mentioned before..e.g. |x| the y values have to be positive
√n where n is any positive number .. the domain is +
-√n where n is any positive number .. the domain is -

etc..

 

[InteGrand]

???Im pree sure there are rules for range given that there are rules for domain

Anyways give me an example of "Inspetion"? It's so consuing when you said that integrand

E.g. "find the range of y = 1/√(x)".

Answer by inspection is the set of all positive reals.

 

[Paradoxica]

Inspection.

Basically this.

 

[eyeseeyou]

We have 4 rules for Domain:

1.Fraction. Bottom cannot equal to zero
2. Surds. Squareroot of bracketed equation, bracketed equaion is greater than or equal to zero
3.Logs. log (bracketed equation). Bracketed equation is greater than 0
4. Inverse trig. Later

What would the rules be for the range?

Doesn't have to be "By inspection". To find the range, all you do is find the domain using the rules I typed up above and just sub it back in the equation in order to find the y value

 

[Nailgun]

Doesn't have to be "By inspection". To find the range, all you do is find the domain using the rules I typed up above and just sub it back in the equation in order to find the y value

you tell em

 

[Paradoxica]

Doesn't have to be "By inspection". To find the range, all you do is find the domain using the rules I typed up above and just sub it back in the equation in order to find the y value

That's not going to work for an arbitrary composition of elementary functions.

Determine the total range of xe^x using your supposed "rules" above.

 

[eyeseeyou]

That's not going to work for an arbitrary composition of elementary functions.

Determine the total range of xe^x using your supposed "rules" above.

I think that would be all values b/c think of it like this, if you were to find the domain and range of an exponential curve then it'd be all values of x and the range would be all values for y so in some cases, you are required to do things by inspection wheras for the rules I typed up above, you aren't really required to

 

[Paradoxica]

I think that would be all values b/c think of it like this, if you were to find the domain and range of an exponential curve then it'd be all values of x and the range would be all values for y so in some cases, you are required to do things by inspection wheras for the rules I typed up above, you aren't really required to

Then don't present rules as universal when they are clearly not.

 

[eyeseeyou]

Then don't present rules as universal when they are clearly not.

It was only 4, not rules for everything (and they were specific)