What is the relationship between the domain and range of a function?

[swatmedic05]

Could someone please explain to me what the range and domain of a function is and how to find them? I just don't understand what they mean
Thank You

 

[Mark44]

The domain of a function is the set of all valid inputs to the function. The range is the set of all possible outputs.

For example, if f(x) = 1/x², the domain is all real numbers except 0. The range is all real numbers greater than 0.

D = {x in R | x \neq 0}
R = {y in R | y > 0}

 

[Willian93]

Domain is all the possible values that X could be
Range is all the possible values that Y could be

example: determine the domain and range of y= x^2

when u sketched the graph, you can see x could be anything, it keeps going forever there for D( -infinity, +infinity)

for y, however, you can see y never goes below x axis, the maximum value for y is just 0
therefore (0, +infinity), because y goes up forever.

 

[swatmedic05]

But domain and range can't share a common number Can they?

 

[Mark44]

But domain and range can't share a common number Can they?

Sure, why not?

 

[HallsofIvy]

But domain and range can't share a common number Can they?

They don't have to but they certainly can.

For example, the domain and range of f(x)= 2x+ 1 are both "all real numbers". Given any real number, I can certainly multiply it by 2 and then add 1- the domain is all real numbers. On the other hand, for any real number x, f(x)= 2x+ 1= y if 2x= y- 1 or x= (y- 1)/2 which is a real number. Since I can get any real number as a result of f(x) the range is all real numbers.