how do u find the domain and range for any function?

Answer 1

In every equation or function defenition there are at least two variables, most commonly x &[ y or f(x)]. Usually in the form y or f(x), short for function of x, = some expression with x in it. the x in the expression on the right, containing the x, is called the independant variable because it can be anything you want from + infinity to - infinity and these values exist in the x DOMAIN. so the f(x) or y on the left of the equation has a value depending on what was chosen for x so it is the dependant veriable and its values are the RANGE of possible values. Now there are at least three occasions this is not true because the RANGE, dependant value, f(x) or y, is undefined. These are:

if x is in the denominator of an expression and its value causes the denominator to equal zero. This is not allowed becuase division by 0 is not allowed and the answer is undefined.

if x is in an expression or by itself, and under a square root, this causes a negative value under the square root. The negative of square roots also do not exist except in an imaginary relm using the i operator.

if x is negative, or is in an expression and its value causes the expression to go negative, and either case is to the right of a natural log (ln) function, or log to any base for that matter, because the logs of negative numbers do not exist.

In summary the DOMAIN is the seed value of a function, the value plugged in for x to evaluate the given function, and can be anything that doesn't cause any of the math operation violations mentioned above.
And the RANGE is the resulting value from the seed value of x as long as the result is not one that is undefinable because of using a disallowed value for x that causes one of the operation violations mentioned above.

Answer 2

There isn't a single trick such as a formula you can do for them, but this is the process I use. If the function is in the form where f(x) (or y) is set equal to the function, you're ready to find the domain; otherwise you must put it in this format.

Now figure out how an answer for the function could not exist. If the equation has a fraction with any variables on the bottom, figure out how to make the denominator equal to zero. Since you cannot divide by zero, no answer can be returned for the function so that x value is not possible. For example, if you have just y=1/x, you would say that the domain is { x | x =/= 0 }.

Then you figure out if this makes any y values impossible. I have no idea if you've done limits, but if it's a continuous function you find the limit as x approaches the value it cannot be from either side as the two limits are equal. This gives you the value that y would be at that point. As long as no other x value returns that y value, that is out of the range.

You can also figure this out using logic. For example, if we were using the y=1/x example, we know that as x gets close to zero, y gets closer to zero. However, you can't divide 1 by anything to get zero as an answer, so this value is impossible.

If you're doing inequalities, you use a completely different method so specify if you are and I can help you there too.

Answer 3

the domain is for what values of x the function exists
and the range is for what values of y the function exists.

there isnt a single formula to let u find the domain and range for a function.