One may be confused when given a function rule to get it's range from it. It's very simple as far as you follow carefully.

Consider the function

Notice that there is no output number when the input number is 3 , since division by zero is meaningless.

This means x can have any value except 3. We say that 3 is not in the domain of the function f.

The otherwise could be example, one could be given g(x) = 3x + 7 for x > 2. Then the domain is the interval (2,∞). If it were not for the restriction on the domain, it would have a domain of (-∞,∞).

We call the set of all inputs of a function its domain, and we call the set of all outputs of a function its range.

It is much easier, in general, to look at the equation of a function and figure out its domain than it is to figure out its range.

For example, if

f(x) = x + 2

______

x - 3.

We can see that its domain is all real numbers except 3. And {x=R,x≠3} in interval notation.

However, it is not as easy to see what the the range must be. A good technique to use is to replace the f(x) in the equation with y and solve the equation for x(make x the subject). It would look this way:

Thus one can see that the output number can be anything except 1. Thus, the range of the function is all real numbers except 1. Range = {y:y=R,y≠1}

Goodluck!

Consider the function

f(x) = 5

____

x-3

. ____

x-3

Notice that there is no output number when the input number is 3 , since division by zero is meaningless.

Quote

File image of an elementary function

This means x can have any value except 3. We say that 3 is not in the domain of the function f.

**The domain of a function contains every possible input number**unless otherwise specified.The otherwise could be example, one could be given g(x) = 3x + 7 for x > 2. Then the domain is the interval (2,∞). If it were not for the restriction on the domain, it would have a domain of (-∞,∞).

**The range of a function**We call the set of all inputs of a function its domain, and we call the set of all outputs of a function its range.

It is much easier, in general, to look at the equation of a function and figure out its domain than it is to figure out its range.

For example, if

f(x) = x + 2

______

x - 3.

We can see that its domain is all real numbers except 3. And {x=R,x≠3} in interval notation.

However, it is not as easy to see what the the range must be. A good technique to use is to replace the f(x) in the equation with y and solve the equation for x(make x the subject). It would look this way:

x = 3y + 2

____

y - 1

____

y - 1

Thus one can see that the output number can be anything except 1. Thus, the range of the function is all real numbers except 1. Range = {y:y=R,y≠1}

Goodluck!