FUN010 · Functions & graphs · Classes 10–12
Reciprocal Function
The reciprocal function y = k/x has two branches (a hyperbola). It is never defined at x = 0 and gets close to both axes without touching them.
1/xReciprocal Function
📐 Formula
f(x) = k/x, x ≠ 0; asymptotes x = 0 and y = 0
✏️ Worked example
k = 2, x = 4: y = 2/4 = 0.5.
🌍 Where it is used
Speed and time for a fixed distance, pressure and volume (Boyle's law).
❓ Quick check
Where is y = 1/x undefined?
🏋️ Practice
EasyFor y = 6/x, find y when x = 3.
Answer: 2
MediumA trip of 120 km at speed v takes t = 120/v hours. Find t at 60 km/h.
Answer: 2 hours
ChallengeIs y = k/x increasing or decreasing for x > 0 when k > 0?
Answer: Decreasing