Question

Explain the domain and range of a function. Under what circumstances would the domain be something other than all real numbers? Provide an example.

Answer 1

domain is the set of all possible values of x, while range is the set of all possible values of y.
for example, y = x^2
since any values of x can be substituted here, we say that the domain is all real numbers (zero, positive and negative numbers -- any number actually )
while the range will be from zero to positive infinity since y cannot be zero because the value of x^2 is always positive (including zero of course; when x = 0, y = 0)

an example of a function where the domain is not all real numbers would be
y = sqrt(x-3)
note that x cannot be less than 3, since the term inside the squareroot will be negative. for example, if we take x = 2
y = sqrt(2-3) = sqrt(-1) = imaginary / does not exist
thus the domain of this would be x is greater than or equal to 3, or in symbols,
[3, +infinity)

hope this helps~ :)