Quick answer
The domain is the set of allowed inputs. The range is the set of outputs a function actually produces.
Start with a small table
For f(x) = x² and domain {-2, -1, 0, 1, 2}, the outputs are {4, 1, 0, 1, 4}. The range is {0, 1, 4}.
A repeated output is allowed
Both -2 and 2 give output 4. That does not violate the definition of a function.
Watch for restrictions
For f(x) = 1/x over real numbers, x cannot equal zero because division by zero is undefined.
Worked examples
f(x)=x+1, inputs {1,2} → outputs {2,3}f(x)=x², inputs {-1,1} → range {1}f(x)=1/x → x ≠ 0
Common mistake to avoid
Do not assume the range always contains as many distinct values as the domain.
Practice questions
Try these without looking at the answers first. Explain your reasoning aloud or write each step.
- Question:
Domain of 1/x: is 0 allowed?— Answer:No - Question:
Range for x² on {-2,0,2}— Answer:{0, 4} - Question:
Is a repeated output permitted?— Answer:Yes
What to learn next
Review the related lessons linked below, then practice independently. If you make an error, write down which rule you used and why it did not apply.