This is the learning layer. Read each heading, try to recall it, then tap Show me to check. No scores, no pressure — peek as often as you like. When you can do these without looking, head to the Flashcards and Tick the Box to test yourself.
Every x has ONE y only.
Input = x = domain
Output = y = range
The send set — used or not.
#A ≤ #B
Not all the co-domain is used — the second set idles.
#A ≥ #B
Many to one — many inputs → the same output.
#A = #B
One-to-one — both injective and surjective.
f∘g(x) = f(g(x)) — do g FIRST.
Swap x & y, then solve for y.
f−1(x) ≠ 1f(x)
f∘g ≠ g∘f
Sub x in directly.
If 00, factorise and cancel the common factor.
Multiply by the conjugate (top or bottom).
Divide above & below by the HIGHEST power of x.
limx→∞ 1x = 0
limx→0 1x = ∞
anything ÷ ∞ = 0