Mathematics · Grades 10–12
Functions: domains and transformations · revision card
Over real numbers, denominators cannot be zero and even-root inputs must be nonnegative.
Keep these ideas clear
Domain restrictions
Over real numbers, denominators cannot be zero and even-root inputs must be nonnegative.
Function notation
f(x) denotes an output, not f multiplied by x.
Two useful examples
For f(x) = 1/(x − 4), which input is excluded?
4
4
For f(x) = √(x − 3), the real domain is
x ≥ 3
x ≥ 3
Explain it without looking
- A graph appears to approach a value but has a hole at the input. Distinguish a limit from a function value.
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.