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